Question

The perimeter of the two squares is 24 cm and 32 cm. If the area of the third square is equal to the sum of the areas of the first two squares, then find the perimeter of the third square.
1. 48 cm
2. 32 cm
3. 45 cm
4. 40 cm

Answer 1

Correct Answer - Option 4 : 40 cm

Given:

The perimeter of two squares respectively = 24 cm ,32 cm

The perimeter of third square = the sum of the area of first and second square

Formula used:

Area of square = side × side 

Calculation:

Let, perimeter of first square = 24 cm

Now 4 × one side = 24 

one side = 24/4 = 6 cm

In second square perimeter = 32 cm

4 × one side = 32

One side = 32/4 = 8 cm

Now area of first square = 6 × 6 = 36 cm²

And second = 8 × 8 = 64 cm² 

In question given that,

Third square area = sum of areas of first and second square

So, third area = 36 + 64 = 100 cm²

Now third area = side × side = 100 cm²

Let side = A

So A² = 100

A = √100 = 10 cm

Now perimeter = 4 × one side = 4 × 10 = 40 cm

∴ Perimeter of third square = 40cm