Question
Calculate the value of x.
- 19.8
- 20
- 14
- 24.2
Hint:
We are given a right-angled triangle. One of its angle is 45°, so the other angle will be 45°. It is 45°-45°-90° triangle. We are given the length of the hypotenuse. We are asked to find the length of its side. We have to use the properties of both right-angled triangle and 45°-45°-90° triangle.
The correct answer is: 19.8
Let the given triangle be ABC
∠ABC = 90°
AB = x
BC =x
AC = 28
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.
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
(28)2 = x2 + x2
784 = 2x2
Dividing by 2 and rearranging we get,
x2 = 392
x2 = 2 × 196
Taking square root we get,
x = 14√2
So, value of x is 14√2.
For such questions, we should know properties of right-angled triangles.
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