Question

a rectangles width is one - fourth of its length. its area is 9 square units. the equation (l(\frac{1}{4}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

Explanation:

Step1: Simplify the left - hand side of the equation

Given the equation $l(\frac{1}{4}l)=9$. Multiply the terms on the left - hand side: $\frac{1}{4}l^{2}=9$.

Step2: Solve for $l^{2}$

Multiply both sides of the equation $\frac{1}{4}l^{2}=9$ by 4 to get $l^{2}=9\times4 = 36$.

Step3: Solve for $l$

Take the square root of both sides. Since $l$ represents the length of a rectangle (a non - negative quantity), $l=\sqrt{36}=6$.

Answer:

6 units