Question

In ∆ABC : AB=24cm, AC=26cm and ∠B = 90°. Find BC

Answer 1

Given:-

• AB of triangle ABC is 24 cm.
• AC of triangle ABC is 26 cm.
• ∠B of triangle ABC is 90°.

To find:-

• Measure of BC.

Solution:-

We know that,

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

Perpendicular = AB = 24 cm.

Hypotenuse = AC = 26 cm

Put, the values in Pythagoras theorem :

$\longrightarrow \sf \bold{{(26)}^{2} = {(BC)}^{2} + {(24)}^{2}}$

$\longrightarrow \sf \bold{676 = {(BC)}^{2} + 576}$

$\longrightarrow \sf \bold{676 - 576 = {(BC)}^{2}}$

$\longrightarrow \sf \bold{ \sqrt{100 } = BC}$

$\longrightarrow \sf \bold{ 10 = BC}$

Or, BC = 10

Therefore,

BC of triangle ABC is 10 cm.