Question

find the area of triangle whose length of altitude are given 12 18 15

Answer 1

suppose the triangle is ABC .

Let, AB=c, BC=a and AC=b. are the sides length corresponding to the height 15cm ,10cm and 12cm respectively

Now ,

area of ABC=area of ABC=area of ABC

1/2 (10a)=1/2(12b)=1/2(15c)

10a=12b=15c

a/6=b/5=c/4 since( dividing by lcm of 10,12,15,)

Let a=6k, b=5k and c= 4k (assuming each ratio as equal to k)

Again ,

area of triangle=sq root(s(s-a)(s-b)(s-c)) since(by using herons formula)

1/2 base *height=sq root(s(s-a)(s-b)(s-c))

1/2 *6k*10=k^2 *sq root (7)

by solving this we get k=8/sqroot 7

put the value of k in 6k, 5k and 4k to get the values of the sides of the triangle