Question

Adjacent sides of a rectangle are in the ratio 5:12. If the perimeter of the rectangle is 34 cm, find the length of the diagonal.

Answer 1

Hey mate!! Here's your answer.
_____________________________

Let the length (l) of the rectangle be 5x
And, breadth (bk be 12 x

Then ,
Perimeter
= 2 (l+b)
= 2 (5x + 12x)
= 2 × 17x
= 34x

But, Perimeter(given) = 34 cm

Hence,

34x = 34
=> x = 34/34
=> x = 1

Hence, length = 5x = 5 ×1 = 5cm
Breadth = 12x = 12×1 = 12 cm.


Now, we know that diagonals of rectangle bisect each other at right angles.

Hence, by Pythagoras Theorem,

diagonal²
= length² + breadth²
= 5² + 12²
= 25 + 144
= 169 cm

=> diagonal
= √169
= 13 cm.

Hence, the diagonal of the rectangle measures 13 cm.

Answer 2

Here is your solution

Given :-
ratio 5:12
perimeter is 34cm

Let,
the sides be 5x and 12x.

perimeter of rectangle =2 (l+b)

=>34=2(5x+12x)
=>34=34x
=>x=1

breadth =5x=5×1=5cm
length =12x=12×1=12cm

length of diagonals =5^2+12^2=13cm

hope it helps you