Question
In this 45-45-90 triangle, I have been given the length of a leg. How do I find the length of the hypotenuse?
- It is the same length as the given leg.
- Multiply that leg's length by √2.
- Multiply that leg's length by 2.
- Divide that leg's length by √2.
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. It is denoted by “x”. We have to use the properties of both right-angled triangle and isosceles triangle.
The correct answer is: Multiply that leg's length by √2.
Let the given triangle be ABC
∠ABC = 90°
AB = 4
AC = x
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
x2 = 42 + 42
= 2(4)2
x = √2(4)
x = √2(length of the a leg)
Therefore, to find the length of a 45°-45°-90° triangle, we have to multiply the length of the leg by √2.
For such questions, we should know about the properties of right-angled and isosceles triangle.
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