Question

ABCD is a rectangle if a b 5 cm and ac 13 cm find the perimeter of ABCD

Answer 1

I hope that it will help you .

It's easy. You have to practise.

Answer 2

The perimeter of ABCD is 34 cm.

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Let's understand a few concepts:

To solve the given problem we will use the following formulas:

• Pythagoras Theorem: $\boxed{\bold{AC^2 = AB^2 + BC^2}}}$, where AC = hypotenuse, AB = perpendicular and BC = Base

• $\boxed{\bold{Perimeter\:of\:rectangle = 2 [Length + Breadth]}}$

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Let's solve the given problem:

ABCD is a rectangle

AB = 5 cm

AC = 13 cm

Let "BC" be the other of the rectangle.

By using the Pythagoras theorem, we get

$13^2 = 5^2 + BC^2$

$\implies 169 = 25 + BC^2$

$\implies BC^2 = 169 - 25$

$\implies BC^2 = 144$

$\implies BC = 12\:cm$

Therefore,

The perimeter of rectangle ABCD is,

= $2[AB + BC]$

= $2[12 + 5]$

= $2\times 17$

= $\bold{34\:cm}$

Thus, the perimeter of ABCD is 34 cm.

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