Question
Find the values of x and y. Leave your answer in simplest radical form.
- x=2 y=2
- x=2√3 y=2√3
- x=3 y=3
- x=√6 y=√6
Hint:
We are given a right-angled triangle. One of its angle is 45°, so the other angle will be 45°. It is 45°-45°-90° triangle. We are given the length of the hypotenuse. We are asked to find the length of its sides. We have to use the properties of both right-angled triangle and 45°-45°-90° triangle.
The correct answer is: x=2√3 y=2√3
Let the given triangle be ABC
∠ABC = 90°
AB = x
BC =y
AC = 2√6
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 = x
x = y
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
(2√6)2 = x2 + x2
24 = 2x2
Dividing by 2 and rearranging we get,
x2 = 12
x2 = 3 × 4
Taking square root we get,
x = 2√3
y = 2√3
So, x = 2√3, y = 2√3
For such questions, we should be know the properties of right-angled triangle and isosceles triangle.
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