Question

1. the perimeter of a rectangle is 90 cm. the length is three times the width. find the dimensions.
2. width:____

length:____

Explanation:

Step1: Set up the variables

Let the width of the rectangle be $w$ cm. Then the length $l = 3w$ cm.

Step2: Use the perimeter formula

The perimeter formula of a rectangle is $P=2(l + w)$. Given $P = 90$ cm, we substitute $l = 3w$ into the formula: $90=2(3w+w)$.

Step3: Simplify the equation

First, simplify the right - hand side: $90 = 2(4w)=8w$.

Step4: Solve for $w$

Divide both sides of the equation $90 = 8w$ by 8: $w=\frac{90}{8}=\frac{45}{4}=11.25$ cm.

Step5: Solve for $l$

Since $l = 3w$, then $l=3\times11.25 = 33.75$ cm.

Answer:

width: $11.25$ cm
length: $33.75$ cm