**Grade 7 math worksheet 4 answers :**

Here we are going to see solutions of 7th grade math worksheet 3.

**Question 1 :**

A tree is broken at a height of 5 m from the ground and its top touches the ground at a distance of 12 m from the base of the tree. Find the length of broken part.

(A) 13 m (B) 15 m (C) 18 m

**Solution :**

Here,

AC^{2} = AB^{2} + BC^{2}

AC^{2} = 12^{2} + 5^{2}

AC^{2} = 144 + 25 ==> 169

AC = √169 = √13 ⋅ 13

AC = 13 m

Hence the length of the broken part is 13 m.

**Question 2 :**

Find the ratio of 3 km to 300 m.

(A) 10:1 (B) 1:10 (C) 2:5

**Solution :**

We can compare two ratios of the same kind only.For that let us convert km to meters

1000 m = 1 km

3 km = 3 x 1000 = 3000 m

= 3000 : 300

= 10 : 1

**Question 3 :**

Find BC, if the area of the triangle ABC is 36 cm^{2} and the height AD is 3 cm.

(A) 18 cm (B) 24 cm (C) 10 cm

**Solution :**

BC = Base of the triangle

AD = Height of the triangle = 3 cm

Area of triangle = (1/2) x Base x Height

= (1/2) x BC x AD

36 = (1/2) x BC x 3

(36 ⋅ 2)/3 = BC

BC = 24 cm

Hence the base of the triangle is 24 cm.

**Question 4 :**

How many times a wheel of radius 28 cm must rotate to go 352 m? (Take π = 22/7)

(A) 300 times (B) 200 times (C) 400 times

**Solution :**

Radius of wheel = 28 cm

Distance to be covered = 352 m = 35200 cm

Distance covered in one revolution = 2πr

= 2 ⋅ (22/7) ⋅ 28

= 176 cm

Number of revolutions

= Distance to be covered/Distance covered in one revolution

= 35200/176

= 200 times

**Question 5 :**

A rectangular park is 45 m long and 30 m wide. The path 2.5 m wide is constructed outside the park. Find the area of that path.

(A) 400 m^{2} (B) 200 m^{2} (C) 150 m^{2}

**Solution :**

Area of path

= Area of rectangle ABCD - Area of rectangle abcd

In abcd : Length = 45 m Width = 30 m |
In ABCD : Length AB = 45 + 2.5 + 2.5 = 50 m Width BC = 30 + 2.5 + 2.5 = 35 m |

Area of path = 50 ⋅ 35 - 45 ⋅ 30

= 1750 - 1350

= 400 m^{2}

**Question 6 :**

Find the value of the expression a^{2} + 2 ab + b^{2},

if a = 3, b = 2

**(A) 27 (B) 35 (C) 25**

**Solution :**

a^{2} + 2 ab + b^{2} = 3^{2} + 2 (3)(2) + 2^{2}

= 9 + 12 + 4

= 25

Let us look into the solution of next problem on "Grade 7 math worksheet 4 answers".

**Question 7 :**

In a computer lab, there are 3 computers for every 6 students. How many computers will be needed for 24 students?

**(A) 27 (B) 35 (C) 25**

**Solution :**

There are 3 computers for every 6 students

Number of computers for 1 student = 3/6 = 1/2

Number of computers for 24 students = (1/2) 24

= 12 computers

Hence every 24 students need 12 computers.

**Question 8 :**

The side of an equilateral triangle is 3.5 cm. Find its perimeter.

(A) 5.9 cm (B) 2.7 cm (C) 10.5 cm

**Solution**

Side length of equilateral triangle = 3.5 cm

Perimeter of equilateral triangle = 3a

= 3 (3.5)

= 10.5 cm

**Question 9 :**

Find the value of 2.5 + 5.1

(A) 7.6 (B) 2.5 (C) 8.2

**Solution**

oooooooooooooooooooooo2.5 (+) ooooooooooooooooooooooo

oooooooooooooooooooooo5.1ooooooooooooooooooooooooooo

oooooooooooooooooooo_____ooooooooooooooooooooooooo

oooooooooooooooooooo07.60000oooooooooooooooooooooo

oooooooooooooooooooo_____ooooooooooooooooooooooooo

**Question 10 :**

The wood cutter took 12 minutes to make 3 pieces of a block of wood. How long would be needed to make 5 such pieces?

(A) 50 minutes (B) 20 minutes (C) 30 minutes

**Solution :**

Time taken for wood cutter to cut block of wood into 3 pieces = 12 minutes

Time taken for wood cutter to cut a block of wood into 1 piece = 12/3 = 4 minutes

Time taken for wood cutter to cut a block of wood as 5 pieces = 4 (5) = 20 minutes

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