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:

2 (5x + 12x) = 34

X = 1

then,

I = 5

b = 12

length of diagonal

D^2 = (5)^2 + (12)^2

D^2 = 25 + 144

D^2 = 169

D = 13 cm

Answer 2

Answer:-

Given:

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,

• Length = 12x = 12(1) = 12 cm.

• Breadth = 5x = 5(1) = 5 cm.

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.