Question

the area of a rectangle is 90 in2^. the ratio of the length to the width is 5:2. find the length and the width

Answer 1

Length and width of rectangle is 15 inches and 6 inches respectively

Solution:

Given that area of a rectangle is 90 square inch

Ratio of length to the width = 5: 2.

Need to determine length and width of rectangle.

As ratio of length to the width is 5 : 2

Lets assume length of rectangle = 5x inches and width of rectangle = 2x inches.

The formula for area of rectangle is given as:

`\text { Area of rectangle }=\text { length of rectangle } * \text { width of rectangle}`

Substituting the given value of area of rectangle and assumed value of length and width of rectangle we get:

`\begin{array}{l}{90=5 x * 2 x} \\\\ {=>90=10 x^(2)}\end{array}`

On solving the above expression for x we get

`\begin{array}{l}{=>(90)/(10)=x^(2)} \\\\ {=>x^(2)=9} \\\\ {=>x=√(9)=3}\end{array}`

`\begin{array}{l}{\text { Length of rectangle }=5 * x=5 * 3=15 \text { inches }} \\\\ {\text { Width of rectangle }=2 *} x=2 *} 3=6 \text { inches }}\end{array}`

Hence length and width of rectangle is 15 inches and 6 inches.