Math, asked by Lipun111, 1 year ago

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?

Answers

Answered by Annabeth
110
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
Answered by Cutiepie93
76
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..

:-)
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