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Chapter 2: Problem 153

The length of a rectangle exceeds the width by 13 yards. If the perimeter of the rectangle is 82 yards, what are its dimensions?

Short Answer

Expert verified
The dimensions of the rectangle are: width = 14 yards and length = 27 yards.

Step by step solution

01

Set up the equations

Let's denote the width of the rectangle as \(x\), that means the length would be \(x + 13\). From the definition of the perimeter, which is defined as twice the sum of the length and the width: \(2(x + x + 13)=82 \), that simplifies to: \(2(2x + 13)=82 \)
02

Solve the equation

Simplify the equation and solve for \(x\): \[4x + 26 = 82 \rightarrow 4x = 82 - 26 = 56 \rightarrow x = \frac{56}{4} =14 \] So, the width of the rectangle is 14 yards.
03

Find the length

Substitute the value of \(x\) into \(x + 13\) to find the length: \[14 + 13 = 27 \] So, the length of the rectangle is 27 yards.

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