the perimeter of a rectangular movie screen at a local cinema is 148 feet. if the length of the screen is 30…

the perimeter of a rectangular movie screen at a local cinema is 148 feet. if the length of the screen is 30 feet longer than the width, what is the length of the screen, in feet?

the perimeter of a rectangular movie screen at a local cinema is 148 feet. if the length of the screen is 30 feet longer than the width, what is the length of the screen, in feet?

Answer

Explanation:

Step1: Set up variables

Let the width of the screen be (w) feet. Then the length (l = w + 30) feet. The formula for the perimeter of a rectangle is (P=2(l + w)). Given (P = 148) feet.

Step2: Substitute into the perimeter formula

Substitute (l=w + 30) and (P = 148) into (P=2(l + w)): [ \begin{align*} 148&=2((w + 30)+w)\ 148&=2(2w + 30)\ 148&=4w+60 \end{align*} ]

Step3: Solve for (w)

Subtract 60 from both sides: (148-60 = 4w), so (88 = 4w). Divide both sides by 4: (w=\frac{88}{4}=22) feet.

Step4: Find the length

Since (l=w + 30), substitute (w = 22) into the equation: (l=22 + 30=52) feet.

Answer:

52