# Find the Diagonal of a Rectangle with l=35 and b=12

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

- find the diagonal of a rectangle with l=35 and b=12.
- 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 with l=35 and b=12 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.

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 right triangle are the length and breadth of the rectangle.

Now, separate one right triangle from the rectangle and place it below.

Label the vertices A, B, C of the right triangle whose ∠B = 90°. We see

- base of the right triangle = length of the rectangle
- height of the right triangle = breadth of the rectangle
- hypotenuse of the right triangle = diagonal of the rectangle

Hence,

base = l = 35 cm

height = b = 12 cm and

hypotenuse = diagonal = d cm

The Pythagorean theorem states that the area of the square whose side is the hypotenuse is equal to the sum of the areas of the squares on the other two sides.

Applying Pythagorean theorem on right triangle ABC,

(AC)^{2} = (BC)^{2} + (AB)^{2}

(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.