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

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Length and breadth of a rectangle are in the ratio 12 : 5.

Perimeter of the rectangle = 2(length + breadth)

length of the diagonal

Length and breadth of a rectangle are in the ratio 12 : 5.

[ length of a rectangle is always greater than the breadth and Adjacent sides are nothing but the length and breadth. ]

And,

Perimeter of the rectangle = 2(length + breadth).

Let the length be 12x cm and breadth be 5x cm.

According to the question,

→ 2(12x + 5x) = 34

→ 2 * 17x = 34

→ x = 34/(2 * 17)

→ x = 1

Hence,

We know that,

Diagonal divides a rectangle into two right angled triangles.

Hence,

using Pythagoras Theorem,

we can say that:

Diagonal = √(length)² + (breadth)²

→ Diagonal = √(12)² + (5)²

→ Diagonal = √144 + 25

→ Diagonal = √169

→ Diagonal = 13 cm

Hence, the length of the diagonal will be 13 cm.

I hope it will help you.

Regards.

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