Geometry Squares Question

Question

The length of each side of Square B is 5cm greater than the length of each side of Square A.

The area of Square B is 100cm^2 greater than the area of Square A

Find the Area of Square B

Answer 1

Formula 1) S_b= 5+S_a where S_b is the side of square B and S_a is the side of square A.

Formula 2) S_b² = S_a² + 100

These are not in the same form, so let's use substitution:

(5+S_a))² = S_a² + 100 = 25+ S_a² + 10S_a = S_a² + 100

Using algebra: 10S_{a =} 75 S_a = 7.5

Plugging back means S_b = 12.5 = Area = 156.25

Checking our work: 7.5*7.5 = 56.25, which is 100 less than the area of Square B.

Hope this helps!