Question

the perimeter of a rectangle is 170 meters. if the length of the rectangle is 25 meters more than the width, what are the dimensions of the rectangle? the length of the rectangle is and the width is

Explanation:

Step1: Set up variables

Let the width of the rectangle be $w$ meters. Then the length $l = w + 25$ meters. The perimeter formula for a rectangle is $P=2(l + w)$. Given $P = 170$ meters.

Step2: Substitute into the perimeter formula

Substitute $l=w + 25$ and $P = 170$ into $P = 2(l + w)$:
\[170=2((w + 25)+w)\]

Step3: Simplify the equation

First, simplify the expression inside the parentheses: $170=2(2w + 25)$. Then distribute the 2: $170 = 4w+50$.

Step4: Solve for $w$

Subtract 50 from both sides of the equation: $170−50=4w$, so $120 = 4w$. Divide both sides by 4: $w=\frac{120}{4}=30$ meters.

Step5: Solve for $l$

Since $l=w + 25$, substitute $w = 30$ into this equation. Then $l=30 + 25=55$ meters.

Answer:

The length of the rectangle is 55 meters and the width is 30 meters.