Question

A rectangle's width is one-fourth of its length. Its area is 9 square units. The equation l(l) = 9 can be used to find l, the length of the rectangle. What is the length of the rectangle? 0.75 units 1.5 units 3 units 6 units

Answer 1

6 units

Explanation:

Let the length = L

Then the width = L/4

area = length * width

area = L * L/4 = 9

L^2/4 = 9

L^2 = 36

L = 6 or L = -6

Since we are dealing with a length, we eliminate the negative answer.

Answer: 6 units

P.S. Your equation is incorrect. L(L) = 9 would work for a square with 4 congruent sides and area 9. Here the sides have different lengths. The equation is L(L/4) = 9.

Answer 2

6 units

Explanation:

A rectangle's width is one-fourth of its length.

w = 1/4 l

area is 9 square units

A = l*w = 9

Replacing w with 1/4l

l * (1/4l) = 9

1/4 l^2 = 9

Multiply each side by 4 to clear the fraction

4 * 1/4 l^2 = 4*9

l^2 = 36

Take the square root of each side

sqrt (l^2) = sqrt(36)

l =6