Question
If AB=13 and AD=6, AC=?
- 10
- 28.17
- 2.4
- 24.12
Hint:
We are given a right-angled triangle ABC. 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 AC. To solve this question, we will use the properties of a right-angled triangle.
The correct answer is: 28.17
The point where altitude meets be “D”
From the figure, we can write the values of lengths and angles.
Length of AB = 13
Length of AD = 6
Angle ABC = 90°
Let the value of altitude be “a”.
Let the value of DC be “b”
For ∆ADB we will use Pythagoras theorem.
AB2 = AD2 + DB2
132= 62+ a2
169= 36 + a2
a2 = 169 – 36
= 133
Taking square root
a = 11.53
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 ADB ~ BDC
So, the ratio of their sides will be equal.
Now, DC = 22.15
AC = AD + DC
= 6 + 22.15
= 28.15
So, the value of AC is 28.15.
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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