Question

Sum of the areas of two squares is 157 metre square if the sum of their perimeter is 68 metre find the sides of the two square

Answer 1

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Answer 2

Answer: 6 cm and 11 cm.

Step-by-step explanation:

Let the side of first square is a meter and the side of second cube is b cm,

Thus according to the question,

Sum of their area is 157

⇒ a² + b² = 157

And, the sum of their perimeter is 68,

4a + 4b = 68

⇒ a + b = 17 ⇒ b = 17 - a

By squaring both sides,

a² + b² + 2ab = 289

⇒ 157 + 2ab = 289

⇒ 2ab = 132

⇒ ab = 66

⇒ a(17-a) = 66

⇒ 17 a - a² = 66

⇒ -a² + 17a - 66 =0

⇒ a² - 17a + 66=0

⇒ a² - 11a - 6a + 66 = 0

⇒ a(a-11)-6(a-11)=0

⇒ (a-6)(a-11)=0

⇒ a = 6 or a = 11

Hence, if the side of first square = x = 6 cm,

Side of second square = y = 17 - 6 = 11 cm

And, if if the side of first square = x = 11 cm,

Side of second square = y = 17 - 11 = 6 cm.