Question
Find the value of x.
- 2
- 18
- 2√9
- 9√2
Hint:
We are given a right-angled triangle. It is an isosceles triangle. We are given the length of the hypotenuse. We are asked to find the length of its sides. We have to use the properties of both right-angled triangle and 45°-45°-90° triangle.
The correct answer is: 9√2
Let the given triangle be ABC
∠ABC = 90°
AB = x
BC =x
AC = 18
We are given that the two sides are equal. So, it is an isosceles triangle.
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
(18)2 = x2 + x2
324 = 2x2
Dividing by 2 and rearranging we get,
x2 = 162
x2 = 2 × 81
Taking square root we get,
x = 9√2
So, value of x is 9√2.
For such questions, we should the properties of both right-angled triangle and isosceles triangle.
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