Question
The length of side c is ____________
- 1
- 2
- √2
- √3
Hint:
We are given a right-angled triangle. We are given the length of the one of the side. The length of the other sides are denoted by variables. We have to find the length of hypotenuse. From the figure, we can see the angles have same value. The two sides opposite to the angles are given same too.
The correct answer is: √2
The given triangle is ACB
∠ACB = 90°
AC = 1
BC = a
AB = c
The given triangle has two angles same. And the sides opposite to the angles are equal.
So, the given triangle is an isosceles triangle.
AC = BC
So, a = 1
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.
AB2 = AC2 + BC2
c2 = 12 + 12
c2 = 1 + 1
= 2
Taking the square root we get,
c = √2
Therefore, the side c is √2.
For such questions, we should know the properties of right-angled and isosceles triangle.
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