Question

5.
The perimeter of a crectangle whose one
side is 12cm
and diagonal is 13cm. ​

Answer 1

Given:

• One side of a rectangle is 12cm
• The diagonal of the rectangle is 13cm

To find:

The perimeter of the rectangle

Some properties of a rectangle-

1. A rectangle is a quadrilateral in which all four interior angles are 90°.
2. Two opposite sides are equal and parallel.
3. Two diagonals of the rectangle are equal.

Now,

We can find another side of the rectangle by Pythagoras theorem.

Let the other side be x cm

⇒(x)² + (12)² = (13)²

⇒ x² + 144 = 169

⇒ x² = 169 - 144

⇒ x² = 25

⇒ x = √25

⇒ x = 5 cm

Thus,

Another side of the rectangle is 5 cm

Now,

• The formula to find the perimeter of the rectangle is = 2(length + breadth) units.

= 2(12 + 5)

= 2 * (17)

= 34 cm

Hence,

The perimeter of the rectangle is 34cm.

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More information

• The formula to find the area of the rectangle is = length*breadth unit².

Answer 2

Answer

The perimeter of the rectangle is 34cm

Explanation

One side of a rectangle is 12cm (given)

Diagonal of the rectangle is 13cm (given)

TO FIND:

• The perimeter of the rectangle

We know that each angle of rectangle is ninety degrees.

So, one side be 'n' cm

So, by Pythagoras theorem.

Base² + perpendicular ² = hypothenuse²

=> (n)² + (12)² = (13)²

=> n² + 144 = 169

=> n² = 169 - 144

=> n² = 25

=> n = √25

=> n = 5 cm

Therefore

Another side of the rectangle is 5 cm

Now,

The formula to find the perimeter of the rectangle is

= 2(length + breath) units.

= 2(12 + 5)

= 2 × (17)

= 34 cm