Question

In a right angled triangle with sides a and b and hypotenuse c, the altitude drawn on the hypotenuse is x. Prove that ab = cx.

Answer 1

SOLUTION :  

Given : In a right-angled triangle with sides a and b and hypotenuse c, the altitude drawn on the hypotenuse is x.

Let the ΔABC   be a right angle triangle having sides a and b and hypotenuse c. BD is the altitude drawn on the hypotenuse AC

In ∆ABC ∼∆BDC

[If a perpendicular is drawn from the vertex containing a right angle of a right triangle to the hypotenuse then the triangle on each side of the perpendicular are similar to each other and to the original triangle.]

AB/BD = AC/BC

[Since, triangles are similar ,hence corresponding sides will be proportional]

a/ x = c/b

xc = ab

∴ ab = cx

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Answer 2

Hello user


Let ABC be the triangle with AB = a and BC = b and AC= c

And Let BO = x


So, Area of triangle ABC = 1/2 × AB × BC. .... (1)


Also, taking AC as base , we get

Area of triangle ABC = 1/2 × AD × x .... (2)


Comparing (1) and (2), we get

1/2 × AB × BC= 1/2 × AD × x

ab = cx.



Proved



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