Question

The perimeter of rectangles MATH is 152 cm. Theratio of the length to width is 5:14. What is the widthof the rectangle? What is the area of the rectangle?

Answer 1

Solution:

Given:

$\begin{gathered} \text{The ratio of length to width of a rectangle=5:14} \\ \text{Perimeter}=152\operatorname{cm} \end{gathered}$

Thus,

$\begin{gathered} l\colon w=5\colon14 \\ \frac{l}{w}=\frac{5}{14} \\ \text{Cross multiplying,} \\ w\times5=l\times14 \\ 5w=14l \\ \text{Dividing both sides by 14 to make l subject of the formula,} \\ \frac{5w}{14}=l \\ l=\frac{5w}{14} \end{gathered}$

Also, recall that the perimeter of a rectangle is given by;

$P=2(l+w)$

Hence,

$\begin{gathered} P=2(l+w) \\ 152=2(\frac{5w}{14}+w) \\ \frac{152}{2}=\frac{5w}{14}+\frac{w}{1} \\ 76=\frac{5w+14w}{14} \\ 76=\frac{19w}{14} \\ \text{Cross multiplying,} \\ 76\times14=19w \\ 1064=19w \\ \text{Dividing both sides by 19 to get the value of w,} \\ \frac{1064}{19}=w \\ w=56\operatorname{cm} \\ \\ \\ \text{Substituting the value of w gotten into;} \\ 5w=14l \\ 5\times56=14l \\ 280=14l \\ \text{Dividing both sides by 14 to get the value of }l \\ \frac{280}{14}=l \\ l=20\operatorname{cm} \end{gathered}$

Therefore, the length of the rectangle is 20cm.

The width of the rectangle is 56cm.

To get the area of the rectangle,

$\begin{gathered} \text{Area}=\text{length x width} \\ A=l\times w \\ A=20\times56 \\ A=1120\operatorname{cm} \end{gathered}$

Therefore, the area of the rectangle is 1120 square centimeters.