Question

In a right angled triangle ABC, 0   B 90 and if AB = 6cm, BC = 8cm, find AC.​

Answer 1

➤ Correct Question :-

In a right angled triangle ABC, ∠B 90 and if AB = 6cm, BC = 8cm, find AC.

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★ How to do :-

Here, we are given with the measurements of two sides of a right-angled triangle. We are asked to find the measurement of the hypotenuse side of the right-angled triangle. So, here we are going to use the concept which is only applicable for right-hand triangle. This concept is known as pythagoras theorem. We are given with two sides of a right-angled triangle in which we can easily find the value of the third side i.e, the hypotenuse side. So, let's solve!!

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➤ Solution :-

${\sf \leadsto \underline{\boxed{\sf {AB}^{2} + {BC}^{2} = {AC}^{2}}}}$

Substitute the given values.

${\tt \leadsto {6}^{2} + {8}^{2} = {AC}^{2}}$

Find the square numbers of both values on LHS.

${\tt \leadsto 36 + 64 = {AC}^{2}}$

Add the values on the LHS.

${\tt \leadsto 100 = {AC}^{2}}$

Remove square on RHS and apply square root on LHS.

${\tt \leadsto \sqrt{100} = AC}$

Find the square root of 100 to get the answer.

${\tt \leadsto \pink{\underline{\boxed{\tt AC = 10 \: \: cm}}}}$

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Verification :-

${\sf \leadsto {AB}^{2} + {BC}^{2} = {AC}^{2}}$

Substitute the given values.

${\tt \leadsto {6}^{2} + {8}^{2} = {10}^{2}}$

Find the square values of all the numbers.

${\tt \leadsto 36 + 64 = 100}$

Add the values on LHS.

${\tt \leadsto 100 = 100}$

So,

${\sf \leadsto LHS = RHS}$

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Hence solved !!