length and width

Question

The length of a rectangular flower garden is 5 feet more than its width. If the area of the garden is 176 square feet. What are the length and width of the garden?

Answer 1

This can be solved by setting up an equation:

We are told that the length is 5 more feet than the width. This means 5+ width = length

The equation for the area of a rectangle is length * width so:

l * w = area

(5 + w) * w = area

5w + w² = 176

w² + 5w -176 = 0

from here, we need to solve for w, which can be done using quadratic formula:

a = 1

b = 5

c = -176

Therefore,

w = (-b ± √(b^2 - 4ac)) / 2a, which becomes

w = (-5 ± √(5^2 - 4* 1* -176)) / 2*1

w = (-5 ± √(25 + 704)) / 2

w = (-5 ± √(729)) / 2

w = (-5 ± 27) / 2

w = -32/2 or 22/2. Since distance cannot be negative, we know that width would be 11.

since length is 11+5, the length is 16.

So, our length is 16 and width is 11