Find the base and the altitude of the triangle if...?

Question

The base and its altitude are in a ratio of 3:2, and the triangle's area is 48.

PLEASE EXPLAIN!!

Answer 1

The area is given by bh/2, where b is the base of the triangle and h is the height (a.k.a. altitude). Now, it's specified that the area is 48 and the base is 3/2 of the height. So this gives a system of equations:

48=bh/2
b=3h/2

Substituting the second equation into the first:

48 = 3h²/4

Multiplying both sides by 4/3:

64=h²

Taking the square root of both sides (and discarding the negative solution, since lengths are never negative):

h=8.

Now substituting that into the second equation:

b = 3(8)/2 = 12

So the base is 12 and the height is 8.

Answer 2

we assume base is a and the altitude is h;see:
a/h = 3/2 ==> a= 1.5 h
area=0.5 * a * h
u said area is 48 so:
48=0.5 * 1.5h * h ==> 48 = (3/4) h^2
==> h^2 = 64 ==> h=8
a=1.5h ==> a=1.5 * 8 =12 ==>
h=8
a=12
got it?

Answer 3

B/H=3/2 ; B=3H/2

A=BH/2 ; A=48

48=BH/2 : B=3H/2
48=(3H/2)H/2
48=(3H^2)/4
H^2=48*4/3
H=8, B=12