A scale drawing of a deck is shown below.

On the actual deck, what is the length, in feet, of AB?

To plant a lawn, Kristin needs 4 pounds of grass seed per 1,000 square feet. A diagram of her lawn is shown below. Kristin wants to plant the flowers in congruent semicircles.

Complete the following in the answer box below:

• How many pounds of seed does Kristin need for her lawn? Use mathematics to explain how you determined your answer. Use words, symbols, or both in your explanation.
   

An artist designed a badge in the shape of a hexagon for a school club. The artist wants to enlarge the badge as shown below.

If the perimeter of the original badge is 18 centimeters, what is the perimeter of the enlarged badge? Round the answer to the nearest centimeter.

A blueprint of a triangular garden with sides measuring 2, 6, and 7 inches is placed on an overhead projector and projected onto a screen, as shown below. The shortest side of the triangle on the screen is 10 inches.

How many inches is the longest side of the triangle on the screen?

The blueprint for a bedroom is shown below. The scale of the blueprint is 1 inch = 4 feet.

What is the length of the longest wall of the bedroom?

The baker has to make enough cakes to serve 100 people. He knows that each person will eat approximately 9 square inches of cake.

• How many heart-shaped cakes should he make?
• Use mathematics to explain how you determined your answer. Use words, symbols, or both in your explanation.

The ratio of the side lengths of two regular pentagons is 3:5. The perimeter of the smaller pentagon is 45 centimeters. What is the perimeter, in centimeters, of the larger pentagon?

In the figure below, trapezoid KLMN is similar to trapezoid RSTU.

What is the length, in units, of ST?

The neighborhood is building a playground with two slides that are similar, as shown below.

What is the length () of the large slide? Round the answer to the nearest foot.

Each hole in the board below has a diameter of 1.250 centimeters. The center of each hole is the vertex of a square.

What is the length () of each side of the square?

• Find the approximate height of the Washington Monument. Use mathematics to explain how you determined your answer. Use words, symbols, or both in your explanation.

In the pictures below, the larger bulletin board is similar to the smaller one.

Note: These figures are not drawn to scale.

What is the perimeter of the larger bulletin board? Round the answer to the nearest foot.

Complete the following in the answer box below:

• Which of the three choices requires the least amount of cardboard? Use mathematics to explain how you determined your answer. Use words, symbols, or both in your explanation.

Trapezoid WXYZ is similar to trapezoid RSPQ. The length of PS is 12 units, the length of SR is 16 units, and the length of XW is 40 units.

What is the length, in units, of XY ?

The triangles shown below are similar and .

What is the length of x ? Round the answer to the nearest tenth of a centimeter.

In the pictures below, the larger bulletin board is similar to the smaller one.

What is the perimeter of the larger bulletin board? Round the answer to the nearest foot.

Terry is enlarging the doll cutout below so it will have a height of 42 centimeters. She wants to make sure that she has a piece of fabric that is wide enough.

What is the minimum width, in centimeters, that Terry needs for the enlarged doll cutout?

The sails of the boat shown below are similar triangles.

Which of these is the height (x) of the smaller sail?

The dimensions of the rectangular pool shown below are 40 yards by 20 yards. Fencing was ordered to enclose the deck. The ratio of the dimensions of the region that is fenced in to the dimensions of the pool is .

• What are the dimensions, in yards, of the region that is fenced in? Use mathematics to explain how you determined your answer. Use words, symbols, or both in your explanation.
   
• How many yards of fence were purchased to enclose the deck?
   
• Fencing costs $7.50 per yard. How much did it cost to purchase fencing to enclose the deck?
   

A house measuring 24 feet by 60 feet contains a room that is similar in shape to the house. The ratio of the dimensions of the room to those of the house is 1:6.

What are the dimensions of the room?

Two jogging paths go around the perimeters of two similar triangles in a park. The dimensions of the path around the smaller triangle are shown in the figure below. One complete lap around the outer edge of the longer path is 3,600 yards.

Use the answer box to complete the following. (You will need to use additional paper to complete the answer satisfactorily.)

• What are the dimensions of the path around the larger triangle?
   
• Use mathematics to justify your answer.

A scale model of a sports car is the size of the actual car. On the actual car, the diameter of each tire is 48 centimeters. What is the circumference, in centimeters, of each tire on the scale model?

The scale of the blueprints for a family's new house is ¼ inch = 4 feet. The family's rectangular kitchen is 8 feet by 12 feet. What are the dimensions of the kitchen on the blueprint?

A gardener uses 20 gallons of water each week on his 8-foot by 10-foot vegetable garden. He plans to enlarge his garden to 24 feet by 30 feet.

Use the answer box to complete the following. (You will need to use additional paper to complete the answer satisfactorily.)

• How much water would he expect to use on his new garden? Use mathematics to explain how you determined your answer. Use words, symbols, or both in your explanation.

The scale drawing for a deck and the diagram of the actual deck are shown below. The deck has a railing with an opening indicated by the dotted line.

What is the total length of the railing, excluding the opening, of the actual deck?

Triangle PQR is similar to triangle XYZ.

Note: These figures are not drawn to scale.

What is the length of QR? Round the answer to the nearest tenth of a unit.

The Smiths designed their family room to measure 16 feet by 20 feet. They designed a guest room to have proportional dimensions with an area of 80 square feet.

• What are the dimensions of the guest room? Use mathematics to explain how you determined your answer. Use words, symbols, or both in your explanation.

The height of the St. Louis Gateway Arch is 630 feet. A miniature version of the St. Louis Gateway Arch is sold as a souvenir. The scale factor of the real arch to the souvenir arch is 2,520:1.

What is the height, in inches, of the souvenir arch?

Earth has a diameter of approximately 8,000 miles. Jupiter's diameter is approximately 88,000 miles. How many times greater is the volume of Jupiter than the volume of Earth?

Triangles PQR and STU are similar.

What is the value of x?

A refrigerator has the dimensions 6 feet by 3 feet by 4 feet. A dollhouse and its contents are being built to a scale in which 1 inch represents 2 feet. What should the dimensions of the dollhouse refrigerator be?

• What is the ratio of the smaller triangle's area to the larger triangle's area?
• Use mathematics to justify your answer.

Look at the two cylinders shown below. The ratio of corresponding diameters is equal to the ratio of corresponding heights.

• What is the height of the large cylinder? Use mathematics to explain how you determined your answer. Use words, symbols, or both in your explanation.
   
• Find the ratio of the volumes of the cylinders. Use mathematics to justify your answer.
   

A toy duck is the size of an actual duck. If the actual length of a duck is 24 inches, what is the length of the toy?