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The altitude of a right triangle is 7 cm less than its base. If the hypotenuse is 13 cm, find the other two sides.

Q5.    The altitude of a right triangle is 7 cm less than its base. If the hypotenuse is 13 cm, find the other two sides.

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Let the length of the base of the triangle be b\ cm.

Then, the altitude length will be: b-7\ cm.

Given if hypotenuse is 13\ cm.

Applying the Pythagoras theorem; we get

Hypotenuse^2 = Perpendicular^2 + Base^2

So, (13)^2 = (b-7)^2 +b^2

\Rightarrow 169 = 2b^2+49-14b

\Rightarrow 2b^2-14b-120 = 0  Or  b^2-7b-60 = 0

\Rightarrow b^2-12b+5b-60 = 0

\Rightarrow b(b-12) + 5(b-12) = 0

\Rightarrow (b-12)(b+5) = 0

\Rightarrow b= 12\ or\ -5

But, the length of the base cannot be negative. 

Hence the base length will be 12\ cm.

Therefore, we have

Altitude length = 12cm -7cm = 5cm  and  Base length = 12\ cm

 

 

 

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