Question

The area of a rectangular piece of land is 260 square meters. If the length of the land was 5 meters less and the width was 2 meters more, the shape of the land would be a square

Answer 1

Part A: write an equation to find the width (x) of the land. Show the steps of your work

Answer 2

Write 2 equations to find l and w
Area of the rectangle: l*w = 260 (1) -> l = 260/w
l - 5 = w + 2
260/w - 5 = w + 2 -> 260 - 5w = w^2 + 2w
v^2 + 7w - 260 = 0. Quadratic equations with 2 real roots x1 = -20 (rejected because < 0) and x2 = 13.
l = 260/13 = 20.
Check: 20 - 5 = 13 + 2 Correct.