Question

1. the perimeter of a rectangle is 510 centimeters. the ratio of the length to the width is 3:2. what are the dimensions of this rectangle? e. 150 cm by 105 cm f. 153 cm by 102 cm g. 158 cm by 97 cm h. 165 cm by 90 cm

Explanation:

Step1: Let the length and width

Let the length be \(3x\) cm and the width be \(2x\) cm.

Step2: Use the perimeter formula

The perimeter formula of a rectangle is \(P = 2(l + w)\). Given \(P=510\) cm, so \(2(3x + 2x)=510\).
Simplify the equation: \(2\times5x = 510\), which is \(10x=510\).
Solve for \(x\): \(x=\frac{510}{10}=51\).

Step3: Calculate length and width

Length \(l = 3x=3\times51 = 153\) cm.
Width \(w = 2x=2\times51 = 102\) cm.

Answer:

F. \(153\) cm by \(102\) cm