Question

The length of rectangle is 16cm and diagonal is of 20cm find the area​

Answer 1

Answer:

heyyy Dear here is ur ans ---

see in figure. ..ABCD is rectangle

in which lenth DC = 16 cm

& diagonal AC = 20 cm

fine it's breath AD = ????

As we known each angle of rectangle is 90*

then ,

/\ADC IS a right triangle

so,

$( ad) {}^{2} + (dc) {}^{2} = (ac) {}^{2} \: \: \ \\ : (Pythagoras theorem) \\ (ad) {}^{2} + (16) {}^{2} = (20) {}^{2} \\ (ad) {}^{2} = 400 - 256$

$ad \: = \sqrt{144 } \\ \: \: \: \: = 12 \: cm$

now ,

length =16cm

breath = 12 cm

area OF rectangle = length x breath

$16 \times 12 = 192 {cm}^{2} \: \: \: ans$

Thank you :(((✌✌✌

Answer 2

Question:-

The length of rectangle is 16cm and diagonal is of 20cm find the area

Solution:-

Given:-

1. length of rectangle are 16 cm and diagonal is of 20 cm respectively.

let, AB = CD = 16 cm and

AC = BD = 20 cm.

Find:-

1. Area of rectangle.

we know

The property of rectangle:-

1. interior angles of rectangle are of 90°.

2. opposite side of rectangle are equal.

3. diagonals of rectangle bisect each other at 90°.

4. both diagonals of rectangle are equal.

So now

To find length of side

we use Pythagoras theorem.

=> (AC)² = (AB)² + (BC)²

=> (20)² = (16)² + (BC)²

=> 400 = 256 + (BC)²

=> (BC)²= 400 - 256

=> (BC)² = 144

=> BC = √144

=> BC = 12 cm.

so BC = AD = 12 cm.

we know formula for

=> Area of rectangle = length× breadth

=> Area of rectangle = (AB) × ( BC)

=> Area of rectangle = 16 ×12

=> Area of rectangle = 192 cm²

Hence area of rectangle 192 cm².

i hope it helps you.