# Find the Diagonal of a Rectangle Whose Length is 35 cm and Breadth is 12 cm

By the end of this lesson, you will be able to

- find the diagonal of a rectangle whose length is 35 cm and breadth is 12 cm.
- interpret the relation among the length, breadth and diagonals of a rectangle.

## Finding the diagonal of rectangle

The diagonal of a rectangle is produced by adding two opposite corners at which length and breadth meet. Let us, for example, find the diagonal of a rectangle whose length is 35 cm and breadth is 12 cm by drawing a figure of rectangle with a diagonal.

First, draw a rectangle and one of its diagonals. Then, label the length and the breadth with measurement and its diagonal.

Let length, l = 35 cm, breadth, b = 12 cm and diagonal = d cm.

The one diagonal divides the rectangle into two seperate congruent right triangles whereas length and breadth meet at right angle.

Therefore, the hypotenuse of each right angled triangle is equal to the diagonal of the rectangle and other two sides of the triangle are the length and breadth of the rectangle.

According to pythagorean theorem,

(hypotenuse)^{2} = (length)^{2} + (breadth)^{2}

or, (diagonal)^{2} = (length)^{2} + (breadth)^{2}

or, d^{2} = l^{2} + b^{2}

or, d^{2} = (35)^{2} + (12)^{2}

or, d^{2} = 1225 + 144

or, d^{2} = 1369

or, d = **√**1369

or, d = **√**(37)^{2}

∴ d = 37

Therefore, the diagonal of the rectangle is 37 cm.Hence, the diagonal of a rectangle is 37 cm whose length is 35 cm and breadth is 12 cm.