Question
Find x.
- 12
- √2
- √3
- 6
Hint:
We are given a right-angled triangle. It is also given that the length of the other two sides is equal. It is an isosceles triangle. We are given the length of the hypotenuse. We are asked to find the value of one of its length. It is denoted by “x”. We have to use the properties of both right-angled triangle and isosceles triangle.
The correct answer is: 6
Let the given triangle be ABC
∠ABC = 90°
AB = x
AC = 6√2
The given triangle is an isosceles triangle.
AB = BC
So, BC = x
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
(6√2)2 = x2 + x2
72 = 2x2
Rearranging we get,
2x2 = 72
Dividing both the sides by 2 we get,
x2 = 36
Taking the square root we get
x = 6
Therefore, the value of x is 6.
For such questions, we should know the properties of both of isosceles triangle and right-angled triangle.
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