Question
If SU=20 and SV=12, Find ST?
- 16
- 15.49
- 2.4
- 13.12
Hint:
We are given a right-angled triangle STU. An altitude is drawn from the vertex having the right angle. It divides the base of the triangle into two parts. The values of parts are given. We are asked to find the value of the TS. To solve this question, we will use the properties of a right-angled triangle.
The correct answer is: 15.49
Let the point where altitude meets be “V”
From the figure, we can write the values of lengths and angles.
Length of SU = 20
Length of SV = 12
Angle STU = 90°
VU = SU – SV
= 20 - 12
VU = 8
Let the value of altitude be “a”.
Due to the altitude, two right-angled triangles are formed.
There is a theorem for altitude drawn from the right angle of a right-angled triangle. It states that, “When altitude is drawn from a right angle, two similar triangles are formed. They are similar to each other. They are also similar to the parent triangle”.
Triangle SVT ~ TVU
So, the ratio of their sides will be equal
If we see, TS is a hypotenuse of the ∆TVS
We will use Pythagoras to solve it further. Pythagoras theorem states that, the square of the hypotenuse is equal to sum of the square of the other sides.
TS2 = SV2 + TV2
TS2 = 122 + 9.82
= 144 + 96
= 240
Taking square roots
TS = 15.49
Therefore, the length of the TS is 15.49
To solve such questions, we should know the properties of right-angled triangles and similar triangles. To find the altitude, we can just remember that the square of the altitude is equal to product of the two values
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