Question

Draw a rectangle that has a perimeter of 20 units and an area of 25 square units

Answer 1

Explanation:

For any rectangle the dimensions are given by:

$w:width \\ \\ l:Length$

So the perimeter (P) is given by the following equation:

$P=2(w+l)$

And the area is:

$A=w\times l$

We know that:

$P=20units \\ \\ A=25units^2$

By substituting:

$20=2(w+l) \\ \\ \therefore w+l=10 \ \ldots eq1 \\ \\ \\ 25=w\times l \ldots eq2$

Solving for $w$ from eq1:

$w=10-l$

Substituting into eq2:

$25=(10-l)\times l$

Then:

$\text{Solving for l:} \\ \\ \\ 10l-l^2=25 \\ \\ 10l-l^2-25=25-25 \\ \\ -l^2+10l-25=0 \\ \\ x_{1,\:2}=\frac{-b\pm \sqrt{b^2-4ac}}{2a} \\ \\ \\ a=-1,\:b=10,\:c=-25 \\ \\ \\ l_{1,\:2}=\frac{-10\pm \sqrt{10^2-4\left(-1\right)\left(-25\right)}}{2\left(-1\right)} \\ \\ l_{1,\:2}=\frac{-10\pm \sqrt{0}}{2\left(-1\right)} \\ \\ l=5$

Solving for w:

$w=10-5=5$

So this rectangle is a square and is shown below.