Question

The diagonal of a rectangle is 36cm.If it's breadth is 16cm;find its length and area

Answer 1

length of diagonal of rectangle=36cm
a square+b square=36×36
a^2+16×16=36×36
a^2+256=1296
a^2=1040
a=32.2cm
length=32.2cm
breadth=16 cm
area=32.2×16
area=515.2
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Answer 2

Question:-

The diagonal of a rectangle is 36cm.If it's breadth is 16cm;find its length and area

Solution:-

Given:-

1. breadth of rectangle are 16 cm and diagonal is of 36 cm respectively.

let, AD = BC = 16 cm and

AC = BD = 36 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

=> (36)² = (AB)² + (16)²

=> 1296 = (AB)² + 256

=> (AB)²= 1296 -256

=> (AB)² = 1040

=> AB = √1040 = √16×65

=> AB= 4√65 cm.

so AB = CD= 4√65 cm.

we know formula for

=> Area of rectangle

= length× breadth

=> Area of rectangle = (AB) × ( BC)

=> Area of rectangle = 4√65 × 16

=> Area of rectangle = 64√65 cm²

Hence area of rectangle

64√65 cm².

i hope it helps you.