In a right triangle ABC, <B = 90°. If AB = 5 cm, BC = 12 cm, find AC
Answers
Answer:
Given:
There is a right angled ∆ABC.
The measure of AB = 5cm.
The measure of BC =12cm.
{\underline{\underline{\red{\sf{To\:Find:}}}}}
ToFind:
Measure of side AC .
{\underline{\underline{\red{\sf{Concept\;Used:}}}}}
ConceptUsed:
We will make use of Pythagoras Theorm.
{\underline{\underline{\red{\sf{Answer:}}}}}
Answer:
We are given a right angled triangle .
So , 'Pythagoras Theorem' is applicable here .
Now Pythagoras Theorem is stated as :
The square of hypotenuse is equal to sum of square of other two sides.
\large{\boxed{\red{\sf{\hookrightarrow AC^{2}=AB^{2}+BC^{2}}}}}
↪AC
2
=AB
2
+BC
2
(For figure refer to attachment:)
\sf{\implies AC^{2}=(5cm)^{2}+(12cm)^{2}}⟹AC
2
=(5cm)
2
+(12cm)
2
\sf{\implies AC^{2}=25cm^{2}+144cm^{2}}⟹AC
2
=25cm
2
+144cm
2
\sf{\implies AC^{2}=169cm^{2}}⟹AC
2
=169cm
2
\sf{\implies AC=\sqrt{169cm^{2}}}⟹AC=
169cm
2
{\underline{\boxed{\purple{\sf{\longmapsto AC=13cm}}}}}
⟼AC=13cm
Therefore length of side AC is 13cm.
Note:
Here 5 cm ,12cm & 13cm are Pythagorean Triplet.