# One side of a rectangle is 10 m longer than the adjacent side. The area is 231 m^2. What are the...

## Question:

One side of a rectangle is 10 {eq}m {/eq} longer than the adjacent side. The area is 231 {eq}m^2 {/eq}. What are the dimensions of the rectangle?

## Area of Rectangle:

{eq}\\ {/eq}

A rectangle is a geometrical figure with opposite sides equal and parallel. Let {eq}a \ \& \ b {/eq} be the adjacent sides of a rectangle, so we can calculate the area of rectangle using the formula : {eq}\text{Area}=a\times b . {/eq}

{eq}\\ {/eq}

Given : One side of rectangle is {eq}a {/eq} and the adjacent side is {eq}b=a+10 {/eq}

And, also it is given that Area= {eq}231 \ m^2. {/eq}

As we know that the Area of rectangle is the product of its sides, so according to given condition, we have :-

{eq}231=a(a+10)\\\Rightarrow 231=a^2+10 a\\\Rightarrow a^2+10a-231=0\\\Rightarrow a^2-21a+11a-231=0\\\Rightarrow a(a-21)+11(a-21)=0\\\Rightarrow a=21, \ \text{As} \ a\neq -11 {/eq}

So, the dimensions of rectangles are : {eq}a=21, \ b=31 {/eq}. 