Question

Represent the following situations in the form of quadratic equations : The sum of areas of two squares514cm^2

is and their perimeters differ by 8 cm. We need to find the sides of both the squares.​

Answer 1

Answer:

The sides of the square are 10 cm and 12 cm

Let the sides of square be x and y cm.

Sum of their areas would be x² + y² = 244

The difference in their perimeter would be 4x-4y = 8

=> x-y = 2

x = y+2

Substituting this value of x in the first equation:

(y+2)² + y² = 244

2y² + 4 + 4y = 244

y² + 2y + 2 = 122

y² + 2y -120 = 0

y² -10y + 12 y-120 =0

y(y-10) +12(y-10) = 0

(y+12)(y-10) = 0

y = 10, -12

Discarding the negative value,

y =10

x = y+2, x = 12