Question

the adjacent sides of a rectangle are in the ratio 3:2 , if its perimeter is 98 CM then find its length​

Answer 1

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Step-by-step explanation:

We know that in a triangle the opposite sides are equal.

So let the rectangle be ABCD.

So AB = CD

AD = BC

In the rectangle, AB is the greater side

So, AB:BC = 4:3

Let the measure of the side be x.

Given, perimeter of the rectangle = 98cm

So,

Formula for perimeter of rectangle,

2( l + b )

So, given the relation

$2( 4x + 3x ) = 98$

$2 × 7x = 98$

$7x = 49$

So the length of the rectangle is 4×7 = 28cm

And the breadth of the rectangle is

3 × 7 = 21cm

Now we need to find the length of the diagonal.

In given triangle,

BC = 21cm

and DC = 28cm

So BD can be found by using Pythagoras Theorem, bcz the measure of angles in a rectangle is 90⁰

So, using the Pythagoras Theorem

$BD² = BC² + CD²$

$BD² = (21)² + (28)²$

$BD² = 441 + 784$

$BD² = 1225$

$BD = \sqrt{1225}$

Therefore,

$BD = 35cm$