Question

Find the length of bc in the figure
​

Answer 1

14cm

Explanation:

First, let us divide the figure into 2 triangles ;

(a) Triangle AOB

(b) Triangle AOC

Let us take triangle AOB first.

On observing closely, we notice that angle AOB is 90degree.

Why? We know that the angle AOC is 90 degrees.

Then, angle AOB = 180 degrees - 90 degrees = 90 degrees.

This means that both triangles are right-angled.

Firstly let us find side OA using Pythagoras' Theorem.

In Pythagoras' Theorem, (a)^2 + (b)^2 = (c)^2, where a and b are the sides of the triangle and c is the hypotenuse of the triangle.

--- (OA)^2 + (OB)^2 = (AB)^2

--- (OA)^2 = (AB)^2 - (OB)^2.

--- (OA)^2 = (13)^2 - (5)^2 [AB = 13 cm and OB = 5 cm]

--- (OA)^2 = 169 - 25

--- (OA)^2 = 144 cm^2

--- OA =
`√(144) \\` cm

--- OA = 12 cm.

Now let us go on to triangle AOC.

Here, we need to find OC.

Once again, we will be using Pythagoras' Theorem.

--- (AC)^2 = (OC)^2 + (OA)^2

--- (AC)^2 - (OA)^2 = (OC)^2

--- (15)^2 - (12)^2 = (OC)^2

--- 225 - 144 = (OC)^2

--- 81cm^2 = (OC)^2

--- OC =
`√(81)` cm

--- OC = 9cm

Now, Length of BC = Length of OB + Length of OC

= 5cm + 9cm

= 14cm.