Question

find the area of a triangle whose perimeter is 180cm and two sides are 80cm and 18cm. Also calculate the altitude of the triangle corresponding shortest side

Answer 1

Perimeter of triangle = 180 cm
Let the third side be x
Now.....

80+18+x =180
x=180-98
x= 82 cm

Check it is a right angle triangle or not

By phytogoeras triplet

H square=base square + perpendicular square

82 square = 18 square + 80 square
82×82=18×18+80×80
6724 = 6724
so it is a right angle triangle

Area of triangle= 1/2×h×b
= 1/2×80×18
= 720 cm square
so area of triangle is 720 cm square.

We can done it in one more way
2nd way -

Since all sides are different...This is a SCALEN
triangle
Area of SCALEN triangle is -
=√s(s-a)(s-b)(s-c)
s= semi perimeter= a+b+c/ = perimeter/2
s= 180/2
s = 90 cm

Now ..
√90(90-80)(90-18)(90-82)
=√90×10×72×8
=√9×10×10×8×9×8
Now every number is in pair so take one number of every digit outside the root
= 9×10×8
=720 cm2 is cm square
Area of triangle is 720 cm square