Question

If the length of a rectangle is 16cm and the length of its diagonal is 20cm, then what will be the area of that rectangle?

Answer 1

The Length, breadth and Diagonal of a rectangle form a right-angled triangle with the length and breadth as the perpendicular sides and the diagonal as the hypotenuse.
∴ diagonal² = length² + breadth² (by the Pythagorean theorem)
∴ 20² = 16² + b²
⇒ 20² - 16² = b²
⇒144 = b²
∴ b = √144 cm = 12 cm

Area of rectangle = length × breadth
= (16 × 12)cm²
= 192 cm²

Answer 2

Hlo friend.. Cutiepie Here..

Length l of Rectangle = 16 cm

Diagonal D of rectangle = 20 cm

We have to find breadth of rectangle.

Let the breadth be b.

${(diagonal )}^{2} = {length}^{2} + {breadth}^{2}$

${(20)}^{2} = {(16)}^{2} + {(b)}^{2}$


$400 = 256 + {b}^{2}$

${b}^{2} = 400 - 256$


${b}^{2} = 144$

$b = \sqrt{144}$

$b = 12$


Breadth b of Rectangle = 12 cm

Area of rectangle = length × breadth

= 16 × 12

= 192 cm²


HOPE IT HELPS YOU..

:-)