Question
Calculate the length of x in this 45-45-90 triangle.
- 4√2
- 4
- 8
- 4√3
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: 4√2
Let the given triangle be ABC
∠ABC = 90°
AB = 4
BC = y
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 = 4
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
= (4)2 + (4)2
= 2(4)2
Taking square root we get,
AC = 4√2
Therefore, the value of the hypotenuse is 4√2.
For such questions, we should know the properties of 45°-45°-90° theorem.
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