Question

Difference of Perimeter of The Squares is 20m and sum of areas is 625 cm. Find the sides of the squares in quadratic equation​

Answer 1

Answer:

Let x and y be the side lengths of the two squares. Then we have a nice equation for a circle. (That was unexpected!)

x2+y2=625

The difference between the side lengths is a quarter of the difference in perimeters, and WLOG I’ll let x>y, so

x−y=5

Already, since the first equation is a circle of radius 25, and since the difference between x and y is the difference between the legs of a right triangle whose hypotenuse is 25, I can see there’s a 3–4–5 triangle (times 5) here. This would allow us to guess the answer, but let’s go ahead and do the algebra.

Substituting,

x2+(x−5)2=625

2x2−10x−600=0

x2−5x−300=0

(x+15)(x−20)=0

x is positive, so the solution is x=20. That means y=15. The side lengths of the two squares are 20 and 15.[1]