Newbie

# Sum of the areas of two squares is 544 m² . If the difference of their perimeter is 32 m, find the sides of the two squares.

• 4

CBSE 10th Class Mathematics
Past year question paper
Year 2020
SET 1, Code Number  – 30/5/1
Question Number –  37 [a]
area and perimeter relation
use area and perimeter formula

Share

1. Let the sides of the two squares be x and y (x > Y)

Difference in perimeter is = 32

4x – 4y = 32

x – y = 8

y = x – 8

Sum of area of two squares = 544

x² + y² = 544

x² + (x – 8)² = 544

x² + x² + 64 – 16 x = 544

2x² – 16x = 480

x² – 8x = 240

x² – 8x – 240 = 0

(x – 20) (x + 12) = 0

X = 20,- 12

Side can’t be negative.

So x = 20

y = x – 8 = 20 – 8 = 12

∴ Sides of squares are 20 cm, 12cm

• 5

Let the sides of the two squares be x and y (x > Y)

Difference in perimeter is = 32

4x – 4y = 32

x – y = 8

y = x – 8

Sum of area of two squares = 544

x² + y² = 544

x² + (x – 8)² = 544

x² + x² + 64 – 16 x = 544

2x² – 16x = 480

x² – 8x = 240

x² – 8x – 240 = 0

(x – 20) (x + 12) = 0

X = 20,- 12

Side can’t be negative.

So x = 20

y = x – 8 = 20 – 8 = 12

∴ Sides of squares are 20 cm, 12cm

• 2