Question

The side of a square exceeds the side of another square by 4 cm and the sum of the area of the two squares is 400 sq cm. Find the dimensions of the two squares.

Answer 1

Let the side of the smaller square be x cm.

Then the side of the larger square is x + 4 cm.

Area of smaller square = x²

Area of smaller square = x²

Sum of the areas is 400 cm²

x² + (x + 4)² = 400

x² + (x² + 8x + 16) = 400

2x² + 8x + 16 = 400

2x² + 8x − 384 = 0

x² + 4x − 192 = 0

(x + 16) (x − 12) = 0

x = 12 or x = −16

Side of the smaller square = 12 cm

Side of the larger square = 16 cm