Question

Find the diagonal of a rectangle whose length is 12cm
and area is 60 sq. cm
​

Answer 1

• The diagonal of the rectangle = 13 cm.

Given :

• The length of a rectangle = 12 cm.
• The area of the rectangle = 60 cm².

To Find :

• The diagonal of the rectangle.

Solution :

Let,

The diagonal of the rectangle be x.

According to the question,

A rectangle have a diagonal. That means, a rectangle is divided into two right angled triangle.

By the Pythagoras theorem.

$\star \: \: \underline{ \underline{ \boxed{\bf{ {AB}^{2} + {BC}^{2} = {AC}^{2}} }}}$

We have,

• AB = 12 cm.

First, we need to find the length of the rectangle.

Given,

The area of the rectangle is 60 cm².

We know that,

Area of the rectangle = l × b

Where,

• l = length (AB) = 12 cm.
• b = breadth (BC) = ?

$\star \: \: \: \underline{\bf{Area \: Of \: The \: Rectangle = l \times b}} \\ \\ \implies \bf{60 \: {cm}^{2} = 12 \: cm \times BC } \\ \\ \\ \implies \bf{ \dfrac{60 \: {cm}^{2} }{12 \: cm} = BC} \\ \\ \\ \implies \bf{5 \: cm} = bc \\ \\ \\ \: \: \therefore \bf{ \: Breadth = 5 \: cm}$

Now, we have to find the diagonal of the rectangle.

$\star \: \: \underline{ \underline{ \boxed{ \bf{{AB}^{2} + {BC}^{2} = {AC}^{2} } }}} \\ \\ \implies \bf{ {(12 \: cm)}^{2} + {(5 \: cm)}^{2} = {x}^{2} } \\ \\ \\ \implies \bf{144 \: {cm}^{2} + 25 \: {cm}^{2} = {x}^{2} } \\ \\ \\ \implies \bf{169 \: {cm}^{2} = {x}^{2} } \\ \\ \\ \implies \bf{ \sqrt{169 \: {cm}^{2} } = x } \\ \\ \\ \implies \bf{13 \: cm = x} \\ \\ \\ \: \: \therefore \bf{ \: Diagonal = 13 \: cm}$

Hence,

The diagonal of the rectangle is 13 cm.