Question

☃️☘Find the length of the diagonal of a
rectangle whose breadth and length are 8 cm and 15 cm, respectively.​

Answer 1

• Length of one diagonal of rectangle is 17 cm.

Step-by-step explanation:

Given:-

• Length and Breadth of rectangle are 15 cm and 8 cm respectively.

To find:-

• Length of one diagonal.

Solution:-

Let,

The rectangle be ABCD.

Length of rectangle be AB and Breadth of rectangle be BC.

And AC be diagonal of rectangle.

• We know that, All angles of rectangle are of 90°. So,

∆ABC is right angled triangle which is right angled at B.

According to Pythagoras theorem :

$\boxed{\star \: \sf \bold{Hypotenuse^{2} = Perpendicular^{2} + Base^{2}}}$

Perpendicular = AB = 15 cm.

Base = BC = 8 cm

Hypotenuse = AC = ?

Put the values in Pythagoras theorem :

$\longrightarrow \sf AC^{2} = (8)^{2} + (15)^{2}$

$\longrightarrow \sf AC^{2} = 64 + 225$

$\longrightarrow \sf AC^{2} = 289$

$\longrightarrow \sf AC = \sqrt{289}$

$\longrightarrow \sf \bold{AC = 17}$

AC is side of ∆ABC and AC is diagonal of rectangle ABCD.

Thus,

Length of one diagonal of rectangle is 17 cm.