# Spectrum Math Grade 5 Chapter 8 Lesson 8 Answer Key Problem Solving

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## Spectrum Math Grade 5 Chapter 8 Lesson 8.8 Problem Solving Answers Key

Solve each problem. Show your work.

Question 1.
Mr. Peate is building a rectangular fence around his house. The fence will be 32 feet long and 29 feet wide. What will be the perimeter of the fence?
The perimeter will be ___________ feet.
The perimeter will be 122 feet.

Explanation:
Given that,
Mr. Peate is building a rectangular fence around his house will be 32 feet long and 29 feet wide.
To find the perimeter, add the length of the sides.

To find the perimeter of the rectangle, add all the sides
P = L + W + L + W
The perimeter of the rectangle is 122 ft.

Question 2.
Sherman developed a photo 4 inches wide by 6 inches long. What is the area of the photograph?
The photo is ______________ square inches.
The photo is 24 square inches.

Explanation:
Given that,
Sherman developed a photo 4 inches wide by 6 inches long.
To find the area, multiply the length and width of the figure.

Area A = Length x Width
A = 6 x 4 = 24 sq in.
The area of the rectangle is 24 sq in.

Question 3.
The Williams family bought a house 4,560 square feet in area. The house is 60 feet long. How wide is the house?
The house is ____________ feet wide.
The house is 76 feet wide.

Explanation:
Given that,
The Williams family bought a house 4,560 square feet in area.
The house is 60 feet long.

Area A = Length x Width
4,560 = 60 x w
w = $$\frac{4,560}{60}$$
w = $$\frac{456}{6}$$
w = 76 ft.

Question 4.
Ms. Ferris owns a barn 12 yards long, 9 yards high, and 11 yards wide. If Ms. Ferris’ barn is rectangular, what is the volume of her barn?
The volume of her barn is ____________ cubic yards.
The volume of her barn is 1,188 cubic yards.

Explanation:
Given that,
Ms. Ferris owns a barn 12 yards long, 9 yards high, and 11 yards wide.

Volume = Length x Width x Height
V = 12 x 11 x 9
V = 1,188 cu yds.
The volume of her barn is 1,188 cubic yards.

Question 5.
The storage center sells rectangular storage spaces that are each 200 cubic feet. Each space is 5 feet long and 5 feet wide. What is the height of each storage space?
Each storage space is _____________ feet high.
Each storage space is 8 feet high.

Explanation:
Given that,
The storage center sells rectangular storage spaces that are each 200 cubic feet.
Each space is 5 feet long and 5 feet wide.
Volume = Length x Width x Height
200 = 5 x 5 x h
h = $$\frac{200}{25}$$
h = 8 ft.

Question 6.
A toy doll was sent to Lucy in a box 8 inches long, 5 inches wide, and 15 inches high. What is the volume of the box?
The volume of the box is ____________ cubic inches.
The volume of the box is 600 cubic inches.

Explanation:
Given that,
A toy doll was sent to Lucy in a box 8 inches long, 5 inches wide, and 15 inches high.
Volume = Length x Width x Height
V = 8 x 5 x 15
V = 600 cubic inches.

Solve each problem. Show your work.

Question 1.
A soccer field is a rectangle. If a soccer field is 90 meters long and 45 meters wide, what is the perimeter of the soccer field?
The perimeter of the field is ____________ meters.
The perimeter of the field is 270 meters.

Explanation:
Given that,
A soccer field is 90 meters long and 45 meters wide.

To find the perimeter of the rectangle, add all the sides.
P = L + W + L + W
P = 90 + 45 + 90 + 45
P = 122 ft.
So, the perimeter of the rectangle is 122 ft.

Question 2.
Julie is cutting out triangle pieces for her scrapbook. The sides of the triangle are 3 centimeters by 14 centimeters by 2 centimeters. What is the perimeter of the triangle?
The perimeter of the triangle is ____________ centimeters.
The perimeter of the triangle is 9 centimeters.

Explanation:
Given that,
The sides of the triangular scrap book are 3 centimeters by 14 centimeters by 2 centimeters.

To find the perimeter of the triangle, add all the sides.
P = side 1 + side 2 + side 3
P = 2 + 3 + 4
P = 9 cm.
So, the perimeter of the triangle is 9 cm.

Question 3.
A rectangular town is 4 kilometers wide and 3 kilometers long. How many kilometers is it around the town?
The perimeter is _____________ kilometers.
The perimeter is 14 kilometers.

Explanation:
Given that,
A rectangular town is 4 kilometers wide and 3 kilometers long.

To find the perimeter of the rectangle, add all the sides.
P = 4 + 4 + 3 + 3
P = 14 km.
So, the perimeter of the rectangle is 14 km.

Question 4.
Ian must mow a lawn 15 meters long and 9 meters wide. What is the area that Ian must mow?
Ian must mow an area of ____________ square meters.
Ian must mow an area of 135 square meters.

Explanation:
Given that,
Ian must mow a lawn 15 meters long and 9 meters wide.

Area A = Length x Width
A = 15 x 9
A = 135 square meters.
So, the area of mow is 135 sq mt.

Question 5.
Lea wants to put carpet on her bedroom floor. Her bedroom is 4 meters long and 6 meters wide. How much carpet does Lea need to cover the floor?
Lea needs ____________ square meters of carpet.
Lea needs 24 square meters of carpet.

Explanation:
Lea bedroom is 4 meters long and 6 meters wide.

Area A = Length x Width
A = 4 x 6
A = 24 square meters.
So, Lea needs 24 square meters of carpet.

Question 6.
A swimming pool is 3 meters in depth, 8 meters in length, and 6 meters in width. What is the volume of the swimming pool?
The volume of the swimming pool is ______________ cubic meters.