Question

The length of a rectangle is 5M less than twice the width, and the area of the rectangle is 52 m^2. Find the dimensions of the rectangle. Length:Width:

Answer 1

Let l be the length of the rectangle, then we can set the following equation:

`l=2w-5m\text{.}`

Where w is the width of the rectangle. Now, the formula for the area of a rectangle is:

`A=lw\text{.}`

Solving the above equation for l, we get:

`l=(A)/(w)\text{.}`

Substituting l=A/w in the first equation we get:

`(A)/(w)=2w-5m\text{.}`

Solving for w, and considering that A=52 m²we get:

`\begin{gathered} A=(2w-5m)w, \\ A=2w^2-(5m)w, \\ 52m^2=2w^2-(5m)w, \\ 2w^2-(5m)w-52m^2=0, \\ (2w-13m)(w+4m)=0, \\ w=(13)/(2)m\text{.} \end{gathered}`

Substituting w=4m in the first equation we get:

`l=13m-5m=8m\text{.}`

Answer:

Length: 8 m,

Width: 6.5 m.