Question
The measure of side b is _____________
- 5
- 10√2
- 5√2
- 10√3
Hint:
We are given a right-angled triangle. We are given the length of the hypotenuse of the triangle. The length of the other sides are denoted by variables. From the figure, we can see the angles have same value. We are asked to find the value of one of its side “b”.
The correct answer is: 5√2
The given triangle is ACB
∠ACB = 90°
AC = b
BC = a
AB = 10
The given triangle has two angles same. So, the sides opposite to the angles are equal.
So, the given triangle is an isosceles triangle.
AC = BC
So, a = b
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
(10)2 = a2 + b2
100 = b2 + b2
100 = 2b2
Dividing by 2 and rearranging we get,
b2 = 50
b2 = 25 × 2
Taking square root we get,
b = 5√2
So, value of b is 5√2.
(10)2 = a2 + b2
100 = b2 + b2
100 = 2b2
Dividing by 2 and rearranging we get,
b2 = 50
b2 = 25 × 2
Taking square root we get,
b = 5√2
So, value of b is 5√2.
For such questions, we should know properties of the right-angled triangle and isosceles triangle.
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