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

Answer:

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

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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.