Question

Find the perimeter of a rectangle whose length is $40cm$ and a diagonal is $41cm$.

Answer 1

Given:

In rectangle, Length $\left(l\right)=40cm$,

Diagonal $\left(d\right)=41cm$

Breadth $b=?$

We know that, in a rectangle,

The square of diagonal is equal to sum of the squares of its length and its breadth.

$\Rightarrow d^2=l^2+b^2$

$\Rightarrow (41cm{)}^2=(40cm{)}^2+b^2$

$\Rightarrow 1681c{m}^2-1600c{m}^2=b^2$

$\Rightarrow 81c{m}^2=b^2$

$\Rightarrow \sqrt{81c{m}^2}=b$

$\Rightarrow 9cm=b$

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

$=2(40cm+9cm)$

$=2\left(49cm\right)$

$=98cm$

Hence, the Perimeter of the rectangle is $98cm$