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

`(540)/(P_B)=(7)/(3)`

By using the cross multiplication

`\begin{gathered} P_B*7=540*3 \\ 7P_B=1620 \end{gathered}`

Divide both sides by 7

`\begin{gathered} (7P_B)/(7)=(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