Solving Quadratics by square roots

Question

Bob the builder is building a retaining wall along one side of his rectangular garden. the garden is twice as long as it is wide. It also has an area of 578 square feet. What will be the length of the retaining wall?

Answer 1

l = 2 x w and Area = 578 = l x w = 2w x w = 2 x w² so

2 x w² = 578 and w² = 289 and w = 289^1/2 = 17 and l = 34

Check A = l x w = 34 x 17 = 578

Answer 2

Area of a rectangle = length * width

Bob's rectangular garden has an area of 578 square feet

Let us consider the width as X, the length will be 2X

Using the formula above for the area

578 = 2X * X

578 % 2 = X²

289=X²

X = square root of 289 = 17 feet

Length = 2X = 2 * 17 = 34 feet