Question

the sum of the areas of two squares is 74 cm square . the difference between their lengths is 2 cm. find the sides of two squares​

Answer 1

Let length of square (1) with greater side be A and square (2) with smaller side be a.

It is given that,  

A - a = 2

A = 2 + a ____(i)

Also,

A² + a² = 74

Putting value of A from (i) in (ii) eqⁿ;

(2 + a)² + a² = 74

4 + a² + 4a + a² = 74        {∵ (a + b)² = a² + b² + 2ab }

2a² + 4a - 70 = 0

a² + 2a - 35 = 0

(a + 7) (a - 5) = 0

a = 5     OR     a = -7

But side cannot be negative. So, a = 5 cm.

Putting value of a in (i) eqⁿ;

A = 2 + (5)

A = 7 cm.