In a right angled triangle, the length of the hypotenuse is 20 cm and the length of one side is 12 cm, what is the length of the other side?

Question

Accepted Answer

The correct option is 3:
Let the right-angled triangle have sides $a$, $b$, and hypotenuse $c$. According to the Pythagorean theorem, the square of the hypotenuse is equal to the sum of the squares of the other two sides. This can be written as:
$a^2 + b^2 = c^2$
In this problem, we are given:
Length of the hypotenuse ($c$) = 20 cm
Length of one side ($a$) = 12 cm
We need to find the length of the other side ($b$).

Substitute the given values into the Pythagorean theorem:
$12^2 + b^2 = 20^2$
Calculate the squares:
$144 + b^2 = 400$
To find $b^2$, subtract 144 from 400:
$b^2 = 400 - 144$
$b^2 = 256$
Now, take the square root of 256 to find $b$:
$b = \sqrt{256}$
$b = 16$
So, the length of the other side is 16 cm. This matches Option 3.

The incorrect option is 1:
8 cm is incorrect because if the other side were 8 cm, then $12^2 + 8^2 = 144 + 64 = 208$, which is not $20^2 = 400$.

The incorrect option is 2:
12 cm is incorrect because if the other side were 12 cm, then $12^2 + 12^2 = 144 + 144 = 288$, which is not $20^2 = 400$. Also, if both legs were 12 cm, the hypotenuse would be $\sqrt{288} \approx 16.97$ cm, not 20 cm.

The incorrect option is 4:
20 cm is incorrect because this is the length of the hypotenuse. One of the legs of a right-angled triangle cannot be equal to the hypotenuse, as the hypotenuse is always the longest side. If one side were 20 cm, the hypotenuse would be $\sqrt{12^2 + 20^2} = \sqrt{144 + 400} = \sqrt{544} \approx 23.32$ cm, which is not 20 cm.