General
General
Easy
Question
Find the length of the hypotenuse. leave your answer in simplest radical form.
- 12
- 6
- 5
- 18
Hint:
We are given a right-angled triangle. It is a 45°-45°-90° triangle. We are given the length of one of it’s leg. We are asked to find the value of the hypotenuse. We have to use the properties of both right-angled triangle and 45°-45°-90° triangle.
The correct answer is: 6
Let the given triangle be ABC
∠ABC = 90°
AB = 3√2
It is a 45°-45°-90° triangle. The two angles of the triangle are same. It means the sides opposite to the triangle are equal. When a triangle has two sides equal, it is an isosceles triangle.
The given triangle is an isosceles triangle.
AB = BC
So, BC = 3√2
Now, we will use the Pythagoras theorem. It states that, the square of the hypotenuse is equal to the sum of the square of the two sides.
AC2 = AB2 + BC2
= (3√2)2 + (3√2)2
= 18 + 18
= 36
Taking the square root of both the sides.
AC = 6
Therefore, the value of the hypotenuse is 6.
For such questions, we should know the properties of different triangles.
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