Triangle question- 5th Jan'16

Question

If sides of triangle are !!17, 25 and 28!!. Then greatest altitude is of length?

!!a)" "15!!

!!b)" "21!!

!!c)" "23!!

!!d)" "!!None

Solution

First we need to calculate area of the triangle using Heron's formula.

Semi perimeter = !!(a+b+c)/2!! where !!a,b,c!! are sides of triangle.

!!s = (17+25+28)/2 = 70/2 = 35!!

Now, area of triangle = !!sqrt(s(s-a)(s-b)(s-c)) = sqrt(35(35-17)(35-25)(35-28)) = sqrt(35xx18xx10xx7) = 210!!

We know that altitude of smallest side of triangle is of greatest length.

Area = !!1/2 xx base xx height = 1/2 xx 17 xx h !!

Hence, !!(17h)/2 = 210!!

So, greatest altitude,!!h = 420/17!!