Question

17. The side of square A is 3 cm longer than twice the side of square B. The difference in their areas is
144 sq. cm. Find the sides of the two squares.​

Answer 1

Step-by-step explanation:

Let the side length of one square be x.

Then the side of another square = 2x + 3

According to question,

(2x + 3)2 - x2 = 144

=> 4x2 + 12x + 9 - x2 = 144

=> 3x2 + 12x + 9 - 144 = 0

=> 3x2 + 12x - 135 = 0

=> x2 + 4x - 45 = 0 [The equation is divided by 3]

=> x2 + 9x - 5x - 45 = 0

=> x(x + 9) - 5(x + 9) = 0

=> (x + 9)(x - 5) = 0

=> x = -9, 5

Since the value of length can not be negative

So, x = -9 is not possible.

Hence, x = 5

Now, the side length of one square = 5 cm

And the side of another square = 2 * 5 + 3 = 13 cm