Question

the side of a square exceeds the side of the another square by 4 cm and the sum of the areas of the two squares is 520 sq. cm. the sum of the lengths of sides of both the squares ​

Answer 1

Let the side of one square be x.

Side of other square be (x + 4)

As we know that the sum of the areas of the two squares is 520 cm².

→ x² + (x + 4)² = 520

→ x² + x² + 16 + 8x = 520

→ 2x² + 8x = 504

→ x² + 4x = 252

→ x²+4x-252 = 0

Now, It's time to find the roots of the EQUATION.

→ x²+4x-252 = 0

→ x = [-b ± √(b²–4ac)]/2a

→ x = [-4 ± √(4²–4(-252))]/2

→ x = [-4 ± √(16+1008)]/2

→ x = [-4 ± √(1024)]/2

→ x = [-4 ± 32]/2

→ x = 14, -18

Finally, We wanna find the sum of the lengths of sides of both the squares as;

→ x + (x + 4)

→ 14 + (14 + 4)

→ 14 + 18

→ 32 CM