Question

the ratio of two sides of a rectangle is 3 ratio 4 if its perimeter is 98 cm find the length of each diagonal of the rectangle
the answer will be marked as a brainlist answer​

Answer 1

Answer:

Length= 21 cm

Breadth= 28 cm

Diagonal= 35 cm

Step-by-step explanation:

Let the length and breadth be '3x' and '4x' respectively, since the ratio

of the two sides of the rectangle are 3:4.

We know that the formula of the perimeter of rectangle is,

Perimeter={2(length+breadth)}unit

=> 98cm = {2(3x+4x)}

=> 98cm = {2×7x}

=> 98cm = 14x

=> x = 98/14

=> x = 7

Hence the value of 'x' is 7

Therefore,

Length of the rectangle= (3×7)cm

= 21 cm

Breadth of the rectangle= (4×7)cm

= 28 cm

Using the Pythagoras theorem, we will find the diagonal of the rectangle:-

Diagonal= √breadth²+length² cm

= √28²+21² cm

= √441+784 cm

= √1225 cm

= 35 cm

Hence, the diagonal of the rectangle is 35 cm respectively.

Answer 2

Answer : The side of the diagonal is 35 cm.

Step-by-step explanation:

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

So, let the rectangle be ABCD.(also, refer to the attachment).

So, AB=CD

AD=BC

In my 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,$2(l+b)\\So\ , giving\ the\ relation\\2(4x+3x)=98\\2×7x=98\\7x=49\\x=7$

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 find by using Pythagoras theorem, cuz the measure of angles in a rectangle is 90°.

So, using pythagoras theorem

$BD^2=BC^2+CD^2\\BD^2=(21)^2+(28)^2\\BD^2=441+784\\BD^2=1225\\BD=\sqrt{1225}\\\therefore BD=35cm.$