Question
Find the value of a and b. Leave your answers in simplest radical form.
- a=4 b=2√2
- a=2√2 b=2√2
- a=2√2 b=4
- a=4 b=4
Hint:
We are given a right-angled triangle. It is an isosceles 45°-45°-90° triangle. We are given the length of the hypotenuse. We are asked to find the value of one of its length and hypotenuse. We have to use the properties of both right-angled triangle and 45°-45°-90° triangle.
The correct answer is: a=4 b=2√2
Let the given triangle be ABC
∠ABC = 90°
AB = b
BC = 2√2
AC = a
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, AB = 2√2
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
a2 = (2√2)2 + (2√2)2
a2 =16
Taking the square root we get
a = 4
Therefore, the value of hypotenuse is 4.
So, a = 4, b = 2√2
For such questions, we should know the properties of right-angled triangle and isosceles triangle.
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