Height and base of a right angled triangle are 24 cm and 18 cm find the length of its hypotenuse
Chapter 2 – Pythagoras Theorem- Text Book Solution
Problem Set 2 | Q 1.7 | Page 44
Some question and their alternative answer are given. Select the correct alternative.
Height and base of a right angled triangle are 24 cm and 18 cm find the length of its hypotenuse
24 cm
30 cm
15 cm
18 cm
According to Pythagoras theorem,
\[\left( \text{Hypotenuse} \right)^2 = \left( \text{Base} \right)^2 + \left( \text{Height} \right)^2 \]
\[ = \left( 18 \right)^2 + \left( 24 \right)^2 \]
\[ = 324 + 576\]
\[ = 900\]
\[ \therefore \text{Hypotenuse} = 30\]
Hence, the correct option is 30 cm.
Explanation:-
We can use the Pythagorean theorem to find the length of the hypotenuse of the right-angled triangle.
According to Pythagorean theorem, in a right-angled triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the other two sides (a and b).
That is,
c^2 = a^2 + b^2
Here, we know that the height (a) of the triangle is 24 cm and the base (b) is 18 cm. Therefore,
c^2 = 24^2 + 18^2 c^2 = 576 + 324 c^2 = 900 c = sqrt(900) c = 30
Hence, the length of the hypotenuse of the right-angled triangle is 30 cm. Therefore, option (B) is correct.
Chapter 2 – Pythagoras Theorem- Text Book Solution
Problem Set 2 | Q 1.7 | Page 44