Sum of the areas of two squares is 394 m2. If the difference of their perimeters is 8 m, find the sides of the two squares?
Explanation:
Let sides of the two squares be ‘x’ and ‘y’. x > y
Difference in perimeter = 8 = 4(x - y) ⇒ x – y = 2 …(1)
Sum of areas = 394 = x2 + y2 ⇒ (x - y)2 + 2xy = 394 ⇒ 4 + 2xy = 394 [x – y = 2; from (1)] ⇒ 2xy = 390 ⇒ 2x(x - 2) = 390 [y = x – 2; from (1)] ⇒ x2 – 2x – 195 ⇒ (x - 15)(x + 13) = 0 ⇒ x = 15 or -13 (rejected)
∴ x = 15 and y = 13
Hence, option (b).
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