Question

The area of a rectangle is 50m^2, and the length of the rectangle is 5 m less than three times the width. Find the dimensions of the rectangle.(Length= m)(Width= m)

Answer 1

Given:

Area of the rectangle is 50 sq. m.

The length of the rectangle is 5 m less than three times the width.

That is,

l=3w-5

To find the dimensions:

The formula for the area of the rectangle is , A=lw

Therefore,

`\begin{gathered} A=(3w-5)() \\ 50=3w^2-5w \\ 3w^2-5w-50=0 \\ (3w-15)(3w+10)=0 \\ 3w=15,3w=-10 \\ w=5,w=-(10)/(3) \end{gathered}`

Since, width can not be negative.

So, -10/3 can be neglected.

Hence, w=5

So, the length is,

`\begin{gathered} l=3(5)-5_{} \\ =15-5 \\ =10 \end{gathered}`

Hence, the dimensions are, l=10 m and w=5 m.