Question

A rectangular retaining wall has an area of

15
square feet. The height of the wall is two feet less than its length. Find the height and the length of the wall.

Answer 1

The height of wall is 3 feet and length of wall is 5 feet

Explanation:

Given as :

The Area of retaining wall = 15 square feet

Let The width of wall = W feet

The Height of wall = ( W - 2 ) feet

Now, Area of Rectangle = Height width

Or , 15 ft² = ( W - 2 ) ft × W ft

Or, 15 = W² - 2 W

Or, W² - 2 W - 15 = 0

Or, W² - 5 W + 3 W - 15 = 0

Or, W ( W - 5 ) + 3 ( W - 5 ) = 0

So , ( W - 5 ) ( W + 3 ) = 0

So, W = 5 , - 3

∴ The width of wall = W = 5 feet

And The Height of wall = ( W - 2 ) = 5 - 2 = 3 feet

Hence The height of wall is 3 feet and length of wall is 5 feet. Answer