Question

A rectangle $ABCD$, $AB=12m$ and $AC=13m$. Find the perimeter of the rectangle $ABCD$

Answer 1

$ABCD$ is a rectangle with $AB=12m$ and $AC=13m$.

To find the perimeter of the rectangle length and breadth should be known.

Here,breadth$=12cm$ and length is not given, instead length of diagonal is given.

So, we can find the length of the rectangle by using the Pythagoras theorem.

Step I: Finding the length of the rectangle.

In $△ABD$,

By Pythagoras theorem,

${\left(AC\right)}^2={\left(AB\right)}^2+{\left(BC\right)}^2$

So, ${\left(BC\right)}^2={\left(AC\right)}^2-{\left(AB\right)}^2$

$$\begin{gathered} ={\left(13\right)}^2-{\left(12\right)}^2 \\ =169-144 \\ =25 \end{gathered}$$

$BC=\sqrt{25}$

$=5m$

So length $=5m$.

Now we can find the perimeter of the rectangle.

Step II: Finding the perimeter of the rectangle $ABCD$.

Let $l$ be the length and $b$be the breadth of the rectangle.

Perimeter of the rectangle$=2(l+b)$

$=2(12+5)$

$=2\times 17$

$=34m$

Therefore, the perimeter of the rectangle $ABCD$ is $34m$.