Question

The length, 18 meters, is the answer to the following question.

"The length of a rectangle is three meters longer than its width. The area of the rectangle is 270 square meters. What is the length of the rectangle?"
Rework this problem: Write an equation using ???? as the length (in meters) of the rectangle that would lead to the solution of the problem. Check that the answer above is correct by substituting 18 for ???? in your equation.

Answer 1

L = B + 3 ..................(1)

L × B = 270 m² .................(2)

on solving we get

L = 18 m, B = 15 m

Explanation:

Let the length of the rectangle be L

and,

Width of the rectangle be 'B'

thus,

according to the question

L = B + 3 ..................(1)

And, area of the rectangle = 270 m²

also,

Area of the rectangle = L × B = 270 m² ...........(2)

on substituting 'L' from equation 1 in equation 2, we get

( B + 3 ) × B = 270

or

B² + 3B - 270 = 0

or

B² + 18B - 15B - 270 = 0

or

B( B + 18 ) - 15(B + 18) = 0

or

( B - 15 ) × ( B + 18 ) = 0

thus, we get

B = 15 m (accepted ) and B = -18 m (neglected : since the length cannot be negative)

therefore,

From 1, we get

L = 15 + 3 = 18 m