Question
If the leg of a 45-45-90 triangle is 7 cm long, then its hypotenuse is _____ cm.
- 7√2
- 49√2
- 7
- 7√7
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: 7√2
Let the given triangle be ABC
∠ABC = 90°
AB = 7cm
AC = x cm
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 = 7cm
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 = (7)2 + (7)2
x2 = 2(7)2
Taking square root we get,
x = 7√2
Therefore, the value of the hypotenuse is 7√2 cm.
For such questions, we should know the properties of different triangles.
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