Question

Find the diagonal of a rectangle whose length is 16 cm and area is 192 sq.cm?

Answer 1

Length = 16 cm
Area = 192 cm^2
Breadth = Area/Length = 192/16 = 12 cm
Diagonal length = root(l^2+b^2) = root(256+144) = root400 = 20 cm

Answer 2

Given

area of a rectangle  is 192 sq.cm

length is 16 cm

Find out the diagonal of a rectangle.

To proof

Formula

Area of a rectangle= length × breadth

as given

area =  192 sq.cm

length = 16 cm

put in the above equation

192 =  16× breadth

$breadth = \frac{192}{16}$

breadth = 12cm

now by using the pythagorus theorem

Hypotenuse² = height² + base²

Diagonal ² = length² +breadth²

                =   16 ²  + 12²

                = 256 + 144

                =  400

                = √ 400

               = 20 cm

The diagonal of the rectangle is 20cm.

Hence proved