Question

the sides of a triangle are 120m,170m,250m.find its area and height of the triangle if its base is 250m.

Answer 1

Its Easy

First Find Its Semiperimeter = 120+170+250 = 540/2 = 270 cm

Apply Heron's Formula

Area = Square Root(270*150*100*20) = 9000m2

Now Area Of Triangle  = 1/2*Base*Height

Longest Side = 250m

1/2*250*altitude = 9000

altitude = 9000/125 = 1800/25 = 360/5 = 72 cm

Answer 2

In general Area of a triangle is 1/2 * Height * Base,
And also, If we know all the three sides then Area of triangle is ,
 
$\sqrt{s(s-a)(s-b)(s-c)}$,

Where s = (a+b+c)/2, and a,b,c are sides of triangle,
This formula is known as Heron's Formula,

Now s = (120+170+250)/2 = 270,

Substituting this, In heron's formula, (Remember you can take any side as a,b,c ),

=> Area is,

$\sqrt{270(150)(100)(20)}$,

=> Area is ,

$\sqrt{81000000}$,

=> Area = 9000 m²,

Now we also know that Area is 1/2  * 250 * Height,

So, Equal them to get Height,
=> 9000 = 1/2*250*Height, Solving for height,
=> 72 m,

Therefore the height of the triangle is 72m,

Hope you Understand, Have a Great Day,
Thanking you, Bunti360 !