Question

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

Answer 1

To find the perimeter of the given rectangle, we need its length and breadth.

Since, breadth is not given we need to find the breadth by applying the Pythagoras theorem.

Let’s assume the breadth of the rectangle is b cm.

By pythagoras property of a right angled triangle,

$a^2+b^2=c^2$

⇒ ${40}^2+b^2={41}^2$

⇒ $1600+b^2={41}^2$

⇒$b^2=1681-1600$

⇒ $b^2=81$

⇒ $b=\sqrt{81}=9cm$

We know that, Perimeter of a rectangle = 2(l + b)

⇒ 2(40 cm + 9 cm)

⇒ 2 × 49 = 98 cm

Hence, the perimeter of the rectangle is 98 cm.