Question

Adjacent sides of a rectangle are in the ratio 5: 12, if the perimeter of the rectangle is 68 cm, find the length of the diagonal.​

Answer 1

Answer:

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Given:

Ratio of sides of a rectangle = 5 : 12

Length of Diagonal = 26 cm.

\rule{350}{1}

Let unit be x.

Length = 12x

Breadth = 5x

Now, we know that all the angles of a rectangle are right angles. So, the triangle formed by diagonal and its adjacent sides is also Right angled triangle.

Now, By Pythagoras theorem

⇒ (Diagonal)² = (Length)² + (Breadth)²

⇒ (26)² = (12x)² + (5x)²

⇒ 676 = 144x² + 25x²

⇒ 676 = 169x²

⇒ x² = 676/169

⇒ x² = 4

⇒ x = √4

⇒ x = ±2

We neglect -2 because we know dimension cannot be negative.

So, x = 2

Length = 12x = 12 × 2 = 24 cm

Breadth = 5x = 5 × 2 = 10 cm

\rule{350}{1}

Now, Perimeter = 2(l + b)

⇒ Perimeter = 2(24 + 10)

⇒ Perimeter = 2(34)

⇒ Perimeter = 68 cm

\rule{350}{2}

Hence,

Perimeter of Rectangle = 68 cm

Length of Rectangle = 24 cm

Breadth of Rectangle = 10 cm

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