Question

A rectangular certificate has an area of 35 square inches. Its perimeter is 24 inches. What arethe dimensions of the certificate?

Answer 1

Explanation

Given that the area of the rectangular certificate is 35 inches and its perimeter is 24 inches. Therefore, if L represents the length of the certificate and w represents its width, therefore;

$\begin{gathered} lw=35---1 \\ 2(l+w)=24---2 \end{gathered}$

Therefore, we can say

$l=\frac{35}{w}$

We will substitute the above in equation 2

$\begin{gathered} 2(\frac{35}{w}+w)=24 \\ \frac{70}{w}+2w=24 \\ multiply\text{ though by w} \\ 70+2w^2=24w \\ 2w^2-24w+70=0 \\ 2(w^2-12w+35)=0 \\ w^2-7w-5w+35=0 \\ (w-7)-5(w-7)=0 \\ (w-7)(w-5)=0 \\ w=7\text{ or w=5} \end{gathered}$

Since the width must be shorter than the length therefore the width will be 5 inches.

Hence;

$l=\frac{35}{5}=7$

Answers:

The dimensions are:

Length = 7 inches

Width = 5 inches