Question
Calculate the length of y in this 45-45-90 triangle.
- 8√2
- 4√2
- 4
- 8
Hint:
We are given a right-angled triangle. It is an isosceles 45°-45°-90° 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 “y”. We have to use the properties of both right-angled triangle and 45°-45°-90° triangle.
The correct answer is: 8
Let the given triangle be ABC
∠ABC = 90°
AB = y
BC = x
AC = 8√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 = y
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
(8√2)2 = y2 + y2
128 = 2y2
Rearranging we get,
2y2 = 128
Dividing both the sides by 2 we get,
y2 = 64
Taking the square root we get,
y = 8
Therefore, the value of y is 8.
For such questions, we should know the properties of different triangles.
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