We included **HMH Into Math Grade 4 Answer Key**** PDF** **Module 9 Lesson 3 Find Unknown Measures** to make students experts in learning maths.

## HMH Into Math Grade 4 Module 9 Lesson 3 Answer Key Find Unknown Measures

I Can find the unknown measure of a rectangle given the length of one side and the area or perimeter.

**Step It Out**

1. Leisl is decorating the front window of a shop with a string of lights. She uses 50 feet of lights around the window. The window is 10 feet wide. What is the length of the window?

A. What do you want to find out? ________

Answer:

Length of the window

B. What do you know? __________

Answer:

The perimeter of window = 50 feet

width of window = 10 feet

C. Use the perimeter formula to find the unknown. Write l for the unknown.

Answer:

Perimeter = 2 ( Length + Width )

D. 2 × l is an unknown addend. How can you use the equation to find 2 × l?

2 × l = ___

2 × ___ = 30 What number multiplied by 2 is 30?

l = ___

Answer:

Perimeter = 2 ( Length + Width )

50 = 2 ( Length + 10 )

25 = Length + 10

Length = 15 feet

E. The length of the window is ___ feet.

Answer:

The length of the window is 15 feet.

**Turn and Talk** How do you know if your answer is correct?

**Step It Out**

2. Samuel is decorating a different window in the shop. The window is a rectangle and has an area of 72 square feet. The length of the window is 9 feet. What is the width?

A. What do you want to find out?

____________________

Answer:

Width of window

B. What do you know?

____________________

____________________

Answer:

The window is a rectangle and has an area of 72 square feet.

The length of the window is 9 feet.

C. Use the area formula to find the unknown.

Write w for the unknown measure.

Answer:

Area = Length X Width

72 = 9 X Width

Width = 72/9 = 8

D. The width of the window is _____.

Answer:

The width of the window is 8 feet

**Turn and Talk** How can you find the area of a square with a side that measures 5 inches?

**Check Understanding Math Board**

Question 1.

Elise is painting a stage set that has an area of 48 square feet. The width of the set is 6 feet. What is the length?

____________________

Answer:

Given,

Elise is painting a stage set that has an area of 48 square feet.

The width of the set is 6 feet.

Area = Length X Width

48 = Length X 6

Length = 48/6 = 8

Therefore, Length is 8 feet.

Question 2.

Jada has 38 yards of fencing to put around a paddock for some goats. She has the length set as 10 yards. What is the width of the paddock?

________

Answer:

Given,

Jada has 38 yards of fencing to put around a paddock for some goats.

She has the length set as 10 yards.

Perimeter = 2 ( Length + Width )

38 = 2 ( 10 + Width )

19 = 10 + Width

Width = 19 – 10 = 9

Therefore, Width is 9 feet

**On Your Own**

Question 3.

Cameron is digging up a section of grass to plant a vegetable garden. The garden will be 30 feet long and have a perimeter of 80 feet.

How wide will the garden be? ____

Answer:

Given,

The garden will be 30 feet long and have a perimeter of 80 feet.

Perimeter = 2 (Length + Width)

80 = 2 (30+ Width)

30 + Width = 40

Width = 40 – 30 = 10

Therefore, garden is 10 feet wide.

Question 4.

Jackie is marking off a section of a yard to practice field hockey. The area of the section is 56 square meters. The length is 8 meters. What is the width of the section?

Answer:

Given,

The area of the section is 56 square meters.

The length is 8 meters.

Area = Length X Width

56 = 8 X Width

Width = 56/8 = 7 meter

Therefore, width of the section is 7 meter.

Question 5.

**Reason** The square-shaped plaza at the center of a small village has an area of 100 square meters. How can you find the length of one side of the plaza?

Answer:

Area = side X side

100 = side X side

side = square root of 100

side = 10 m

Thereofore, length of one side of the pizza is 10 meters.

**Use Structure Use the area or perimeter formula to find the unknown measure.**

Question 6.

n = ___

Answer:

Area = Length X Width

20 = n X 4

n = 20/4 = 5 cm

Therefore, value of n is 5 cm

Question 7.

n = ___

Answer:

Perimeter = 2 ( Length + Width )

22 = 2 (7 + n)

7 + n = 11

n = 11-7 = 4

Therefore, value of n is 4 mi.

Question 8.

n = ____

Answer:

Perimeter = 2 ( Length + Width )

40 = 2 (n + 8)

8 + n = 20

n = 20 – 8 = 12

Therefore, value of n is 12 in.

Question 9.

n = ____

Answer:

Area = Length X Width

27 = n X 9

n = 27/9 = 3 ft

Therefore, value of n is 3 ft.

**On Your Own**

Question 10.

**History** Checkers is one of the oldest board games still played today. The oldest known checkerboard is over 5,000 years old. A standard checkerboard is square and has an area of 64 square inches. What is the length of one side of the board? ______

Answer:

Given,

A standard checkerboard is square and has an area of 64 square inches.

Area = Side X Side

64 = side X side

Side = 8 inches

Therefore, the length of one side of the board is 8 inches.

Question 11.

**Open Ended** Write a word problem that involves finding an unknown measure of a rectangle given an area or a perimeter and one length. Include a diagram and the answer.

______________________

______________________

______________________

Answer:

The area of the patio of a relative’s house is 20 square meters.

The width of the patio is 2 meters.

What is the length of the patio?

**Solution:
**The area is A = (w) * (l)

Where,

w: width and l: long

l = A / w

Substituting values:

l = 20/2

l = 10 meters

Question 12.

**Use Structure** A square has a perimeter of 24 inches. How can you find the length of a side?

Answer:

Given,

A square has a perimeter of 24 inches.

Perimeter of square = 2 ( side + side )

4 X side = 24 incges

side = 24/4 = 6 inches

Therefore, the length of a side is 6 inches.

**Use Structure Use the area or perimeter formula to find the unknown measure.**

Question 13.

n = ____

Answer:

Perimeter = 2 ( Length + Width )

16 = 2 ( 6 + n )

6 + n = 8

n = 8 – 6 = 2

Therefore, value of n is 2 cm.

Question 14.

n = ____

Answer:

Area = side X side

n X n = 36

n = 6

Therefore, value of n is 6 in.

Question 15.

n = ____

Answer:

Area = Length X Width

45 = 15 X n

n = 45/15 = 3

Therefore, value of n is 3 m.