Question

question 5 of 10
a rectangles width is 5 feet less than its length. if the area of the rectangle is 546 square feet, what is its length, in feet?

Explanation:

Step1: Define variables

Let the length of the rectangle be \( l \) feet. Then the width \( w = l - 5 \) feet.

Step2: Use area formula

The area of a rectangle is \( A = l \times w \). Substituting the values, we get \( 546 = l(l - 5) \).

Step3: Expand and form quadratic equation

Expanding gives \( l^2 - 5l - 546 = 0 \).

Step4: Solve quadratic equation

We factor the quadratic: \( l^2 - 26l + 21l - 546 = 0 \), \( l(l - 26) + 21(l - 26) = 0 \), \( (l - 26)(l + 21) = 0 \).
So \( l = 26 \) or \( l = -21 \). Since length can't be negative, we take \( l = 26 \).

Answer:

26