In a triangle xyz,xy =7cm,yz=24cm and xz=25cm. Find the length of the perpendicular from vertics y to side xz?
Answers
Given :- In a triangle xyz, xy = 7cm, yz = 24cm and xz = 25cm.
To Find :-
- The length of the perpendicular from vertics y to side xz ?
Solution :-
checking if given sides satisfies the pythagoras condition ,
Let ,
- XY = Perpendicular of ∆XYZ
- YZ = Base of ∆XYZ .
- XZ = Hypotenuse of ∆XYZ .
so,
→ XY² + Y² = XZ² (By pythagoras theorem.)
→ 7² + 24² = 25²
→ 49 + 576 = 625
→ 625 = 625 .
therefore, we can conclude that,
- ∆XYZ is a right angled ∆.
then,
→ Area of Right angled ∆XYZ = (1/2) * Base * Perpendicular height .
Now, Let us assume that, the perpendicular from vertics Y to side XZ(Hypotenuse) is h cm.
therefore,
→ (1/2) * Base(YZ) * Perpendicular height(XY) = (1/2) * Base(XZ) * Perpendicular height(h)
→ (1/2) * 24 * 7 = (1/2) * 25 * h
→ 24 * 7 = 25 * h
→ 25h = 168
→ h = (168/25)
→ h = 6.72 cm. (Ans.)
Hence, the perpendicular from vertics Y to side XZ is 6.72 cm.
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