Question

The perimeter of a rectangle A is 540 inches. The ratio of the lengths ofa large and small rectangle is 7:3. Find the perimeter of rectangle B, thesmaller rectangle. Round to the tenths.

Answer 1

The ratio between the lengths of 2 rectangles is the same between their perimeters

$l_1\colon l_2=P_1\colon P_2$

Since the ratio between the length of rectangle A and the length of rectangle B is 7: 3, then

The ratio between the perimeter of rectangle A to the perimeter of rectangle B is 7: 3 too

$\begin{gathered} l_A\colon l_B=7\colon3 \\ P_A\colon P_B=7\colon3 \end{gathered}$

Since the perimeter of rectangle A is 540, then

$540\colon P_B=7\colon3$

We will write them as a fraction

$\frac{540}{P_B}=\frac{7}{3}$

By using the cross multiplication

$\begin{gathered} P_B\times7=540\times3 \\ 7P_B=1620 \end{gathered}$

Divide both sides by 7

$\begin{gathered} \frac{7P_B}{7}=\frac{1620}{7} \\ P_B=231.4285714 \end{gathered}$

Round it to the nearest tenth

$P_B=231.4\text{ inches}$

The perimeter of the smaller rectangle B is 231.4 inches