Sum of the areas of two squares is 400 cm 2 . If the difference of their perimeters is 16 cm, find the sides of the two squares.

Given: Sum of the areas of two squares = 400 cm 2 . The difference of their perimeters = 16 cm Let `a` and `b` be the sides of 2 square. Sum of Areas, ⇒ a 2 \+ b 2 = 400 ...............(1) Difference of Perimeters, ⇒ 4a \- 4b = 16 ⇒ 4(a \- b) = 16 ⇒ a \- b = ⇒ a \- b = 4 ⇒ a = 4 \+ b Substituting the value of a in equation (1), we get ⇒ (4 \+ b) 2 \+ b 2 = 400 ⇒ 4 2 \+ b 2 \+ 2 x 4 x b \+ b 2 = 400 ⇒ 16 \+ b 2 \+ 8b \+ b 2 = 400 ⇒ 16 \+ 2b 2 \+ 8b \- 400 = 0 ⇒ 2b 2 \+ 8b \- 384 = 0 ⇒ b 2 \+ 4b \- 192 = 0 ⇒ b 2 \+ 16b \- 12b \- 192 = 0 ⇒ b(b \+ 16) \- 12(b \+ 16) = 0 ⇒ (b \+ 16)(b \- 12) = 0 ⇒ b = \- 16 or 12 Since the side of a square cannot be negative, b = 12 cm. So, a = 4 \+ b = 16 cm Hence, the sides of the squares are 16 cm and 12 cm.

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Mathematics

Sum of the areas of two squares is 400 cm². If the difference of their perimeters is 16 cm, find the sides of the two squares.

Mensuration

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A triangle and a parallelogram have the same base and the same area. If the sides of the triangle are 26 cm, 28 cm and 30 cm and the parallelogram stands on the base 28 cm, find the height of the parallelogram.

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Mathematics

Sum of the areas of two squares is 400 cm2. If the difference of their perimeters is 16 cm, find the sides of the two squares.

Mensuration

Related Questions

A triangle and a parallelogram have the same base and the same area. If the sides of the triangle are 26 cm, 28 cm and 30 cm and the parallelogram stands on the base 28 cm, find the height of the parallelogram.

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