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The perimeter of a rectangular piece of metal is $150$ centimeters. The piece is $26$ centimeters wide. How long is it? $\newline$ _____ centimeters

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Area and perimeter: word problems

Full solution

Q. The perimeter of a rectangular piece of metal is

150

centimeters. The piece is

26

centimeters wide. How long is it?

\newline

_____ centimeters

Identify formula: Identify the formula for the perimeter of a rectangle. $\newline$ The formula for the perimeter of a rectangle is $P = 2l + 2w$ , where $P$ is the perimeter, $l$ is the length, and $w$ is the width.
Plug in values: Plug in the values of $P$ and $w$ into the formula. $\newline$ Given $P = 150$ centimeters and $w = 26$ centimeters, we can substitute these values into the formula to get $150 = 2l + 2(26)$ .
Simplify equation: Simplify the equation by performing the multiplication. $150 = 2l + 52$
Isolate term with l: Isolate the term with $l$ by subtracting $52$ from both sides of the equation. $\newline$ $150 - 52 = 2l$ $\newline$ $98 = 2l$
Solve for l: Solve for l by dividing both sides of the equation by $2$ . $\newline$ $\frac{98}{2} = l$ $\newline$ $49 = l$
Check solution: Check the solution by plugging the value of $l$ back into the original perimeter formula. $P = 2l + 2w$ $150 = 2(49) + 2(26)$ $150 = 98 + 52$ $150 = 150$ The solution checks out.

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