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
Deepak BoraNewbie
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.
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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
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