Question

If the length of a diagonal of a rectangle of length 16cm is 20cm, them its area is​

Answer 1

Length l of a rectangle is 16 cm

Diagonal D of a rectangle is 20 cm

We have to find breadth of a rectangle

Let breadth be b

(diagonal)² = (length)² + (breadth)²

(20)² = (16)² + (b)²

400 = 256 + b²

b² = 400 - 256

b² = 144

b = √144

b = 12 cm

Breadth of a rectangle is 12 cm

Area of rectangle = length × breadth

Area of rectangle = 16 × 12

Area of rectangle = 192 cm²

Answer 2

$\huge\bold\purple{\underline{\underline{{Question:-}}}}$

The length of a rectangle is 16 cm and the length of its diagonal is 20 cm. The area of the rectangle is

$\huge\bold\blue{\underline{\underline{{Solution:-}}}}$

•Let ABCD be the rectangular plot.

Then,

⇢ AB = 16 cm and AC = 20 cm BC = ?

According to Pythagoras theorem

From right angle triangle ABC, we have :-

⇢ AC² = AB² + BC²

⇢ (20)² = (16)² + BC²

⇢ BC² = (20)² – (16)²

⇢ BC² = 400 – 256

⇢ BC² = 144

⇢ BC = √144

⇢ BC = 12 cm

Hence, the area of the rectangle plot = (L × b)

Where,

L = 16 cm

b = 12 cm

Then,

⇢ (16 × 12)

⇢ 192 cm²

$\fbox{Area of Rectangular Plot = 192 cm²}$