# Find the area of triangle whose sides are 5cm,12cm and 13cm,aiso find its shortest altitude?

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by nishavini

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by nishavini

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(s(s-a)(s-b)(s-c))^1/2

where s= (a+b+c)/2

but this is aright angled triangle, so you can easily apply the formula area=1/2axb, where a=12, b=5

for altitude, you can imagine it divides the hypotenuse into 2 parts x and 13-x

h,x,5 (h is length of altitude) form a right angled triangle whereas h,13-x,12 form another.

using pythagoras theorm, solve for x.

then find the altitude.

the shortest altitude is the altitude to the hypotenuse.

The Brainliest Answer!

Here Sides are - 5 cm, 12 cm and 13 cm.

So, s = (a+b+c+)/2 where a,b, and c are sides of triangle

s = (5+12+13)/2 = 30/2 = 15

Area =

Area =

So, Area = 30

And the smallest height will be on the largest base. So here the largest side is 13 cm.

So by area formula we have

Area = 1/2 *base * height

But area = 30

so, 30 = 1/2 * 13 *height

height = 60/13 = 4.615 cm