Find the length of the hypotenuse of a right angled triangle if remaining sides are 9 cm and 12 cm.
Chapter 2 – Pythagoras Theorem- Text Book Solution
Problem Set 2 | Q 2.4 | Page 44
Find the length of the hypotenuse of a right angled triangle if remaining sides are 9 cm and 12 cm.
In a right angled triangle,
According to Pythagoras theorem.
\[\left( \text{Hypotenuse} \right)^2 = \left( \text{Base} \right)^2 + \left( \text{Height} \right)^2 \]
\[ = \left( 9 \right)^2 + \left( 12 \right)^2 \]
\[ = 81 + 144\]
\[ = 225\]
\[ \therefore \text{Hypotenuse} = 15 cm\]
Hence, the length of the hypotenuse is 15 cm.
Explanation:-
We can use the Pythagorean theorem to find the length of the hypotenuse of a right-angled triangle if the lengths of the other two sides are given.
According to the Pythagorean theorem, in a right-angled triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the lengths of the other two sides.
In this case, the two sides are 9 cm and 12 cm, and the hypotenuse is the unknown length we need to find. So we have:
hypotenuse^2 = 9^2 + 12^2 hypotenuse^2 = 81 + 144 hypotenuse^2 = 225
Taking the square root of both sides, we get:
hypotenuse = sqrt(225) hypotenuse = 15
Therefore, the length of the hypotenuse of the right-angled triangle is 15 cm.
Chapter 2 – Pythagoras Theorem- Text Book Solution
Problem Set 2 | Q 2.4 | Page 44