Question

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

Answer 1

Heya !!!


Let sides of rectangle be 5X and 12X.



Perimeter of rectangle = 34


2 ( L + B ) = 34



2 ( 12X + 5X) = 34




17X = 17



X = 17/17 = 1 cm



Length of rectangle = 12X = 12 × 1 = 12 cm


And,


Breadth of rectangle = 5X = 5 × 1 = 5 cm


Therefore,


Length of diagonal = ✓(L)²+(B)²



=> ✓(12)² + (5)²



=> ✓144 + 25



=> ✓169


=> 13 cm


★ HOPE IT WILL HELP YOU ★

Answer 2

Hello!!

Here is the answer.

Given that adjacent sides are in ratio 5:12 and perimeter is 34 cm.

Let the common ratio be k.
So, sides will be 5k and 12k.

Now,
P = 2(sum of adjacent sides)
34 = 2 ( 12k + 5k)
34 = 2 (17k)
34 = 34k
k = 1.

So, sides are
12k = 12×1 = 12 cm and 5k = 5 cm.

Now, using Pythagoras theorem.
Diagonal² = base² + altitude²
D² = 12² + 5²
D² =144 + 25
D = √169 = 13 cm.

Hence, the diagonal is 13 cm in length.

Hope It Helps