Question

The area of a Rectangle having length 4cm is
12 cm square
what is the length of its diagonal​

Answer 1

Answer:

Correct Question:

The area of a rectangle having length as 4cm is 12 cm^2. Whar is the length of uts diagonal?

Given:

Length of the rectangle = 4cm

Area of the rectangle = 12cm.

To find:

Length of its diagonal.

Solution:

Since diagonal of a rectangle

$= \sqrt{width {}^{2} + hypotenuse {}^{2} }$

First we need to find width of the rectangle

$= > 2(l + b) = 12 \\ \\ = > 8 + 2b = 12 \\ \\ = > 2b = 12 - 8 \\ \\ = > 2b = 4 \\ \\ = > b = 2 \: cm$

Therefore, width of the rectangle

= 2cm.

We can find the diagonal of a triangle if we have the width and hypotenuse.

Cut the rectangle into two equal right triangles where the hypotenuse of both is the rectangle's diagonal. So, now we need to find hypotenuse of the triangle ABC.

According to pythagoras theorem,

$hypotenuse {}^{2} = {perpendicular}^{2} + base {}^{2}$

$h {}^{2} = 4 {}^{2} + 2 {}^{2} \\ \\ = > h {}^{2} = 16 + 4 \\ \\ = > h {}^{2} = 20 \\ \\ = > h = \sqrt{20} \: cm$

Since hypotenuse = $\sqrt{20} \: cm$

Length of the diagonal of the rectangle

= $\sqrt{20} \: cm$