Question
Find the length of the leg. Leave your answer in simplest radical form.
- 128
- 8√2
- 16
- 2√2
Hint:
We are given a right-angled triangle. One angle is 45°, so remaining angle will be 45°. It is 45°-45°-90° triangle. We are given the length of the hypotenuse. We are asked to find the value of one of its leg. We have to use the properties of both right-angled triangle and 45°-45°-90° triangle.
The correct answer is: 8√2
Let the given triangle be ABC
∠ABC = 90°
Let the value of its leg be “p”.
AB = p
AC = 16
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 = p
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
162 = p2 + p2
256 = 2p2
Rearranging we get,
2p2 = 256
Dividing both the sides by 2 we get,
p2 = 128
p2 = 2 × 64
Taking the square root we get
p = 8√2
Therefore, the value of one of its leg is 8√2.
For such questions, we should know properties of different triangles.
Related Questions to study
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