Question

A photograph is 3 cm longer than it is wide. It's area is 40 cm^2. Find its length and its width.

Answer 1

Given:

A photograph is 3 cm longer than it is wide.

Its area is 40 square cm.

To find:

The length and width.

Step-by-step explanation:

It is given that,

`l=w+3`

Using the formula for the area of the rectangle,

`\begin{gathered} A=lw \\ 40=(w+3)w \\ 40=w^2+3w \\ w^2+3w-40=0 \end{gathered}`

Solving for w we get,

`\begin{gathered} w^2+8w-5x-40=0 \\ w(w+8)-5(w+8)=0 \\ (w+8)(w-5)=0 \\ w=-8,w=5 \end{gathered}`

The width can not be negative.

So, the width is 5cm and the length is,

`l=5+3=8cm`

Final answer:

The width is 5cm and the length is 8cm.