Question

the length of a rectangle is 3 times of its width is the length of the diagonal is 8 square root 10 then the perimeter of the rectangle is

Answer 1

answer is- let breath=x and length=3x
given that diagonal=8√10=√640
we know that by Pythagoras theorem
(√640)^2=x^2+3x^2
640=x^2+9x^2
640=10x^2
64=x^2
8=x
hence sides are8and24
perimeter=2(24+8)
perimeter=64

Answer 2

Given :

The length of a rectangle is 3 times of its width  

The length of the diagonal is 8 square root 10

To Find:

Find the perimeter of the rectangle

Solution:

Let the width of rectangle be x

We are given that length of rectangle is 3 times of its width  

Length of rectangle = 3x

$Diagonal^2 = Length^2+Width^2$

We are given that length of diagonal is $8\sqrt{10}$

$(8\sqrt{10})^2=(3x)^2+x^2\\6400=9x^2+x^2\\6400=10x^2\\640=x^2\\\sqrt{640}=x$

25.29=x

Length of rectangle = 3x =3(25.29)= 75.87 m

Width of rectangle = 25.29 m

Perimeter of rectangle =2(l+b)=2(75.87+25.29)= 202.32 m  

Hence The perimeter of rectangle is 202.32 m