Question

Shashi has a rectangular garden. The length of the garden is 4 feet less than twice the width. The area of the garden is 448 square feet. What is the length of the garden?

Answer 1

28 feet

Explanation:

Area of a rectangle is :

A = L × W

We are given A and a expression for L, so let's substitute :

448 = (2W-4) × W

Now we expand the left side :

2W²-4w = 448

Subtract 448 from both sides :

2W²-4W-448 = 0

Divide everything by 2 :

W²-2W-224 = 0

Now we factorise :

Find 2 numbers that multiply to give -224 and add to give -2 :

-16 and 14

Rewrite -2W with -16W and +14W :

W² - 16W + 14W -224 = 0

W(W-16) +14(W-16) = 0

(W+14)(W-16) = 0

W = -14 , W = 16

Only take positive value since this is lengths :

W = 16

Now we substitute W into the expression to find L :

L = (2W -4)

L = 2(16) - 4

L = 32 - 4

L = 28

Units will be feet since it is a length

Hope this helped and have a good day