Question

The ratio of the base to the height of a triangle is 5:3. The area of the triangle is 120cm. How long is the base?

Answer 1

Answer:

20 cm

Step-by-step explanation:

5n × 3n = 2×120

15n²=240

n²=240/15 =16

n=√16 = 4

base = 5× 4 = 20

Answer 2

line one b=h*5/3

line two b*h/2=120

let's substitute b in line two with the righthand side of line one

(h*5/3)*h/2=120

h²*5/6=120

h²=(120/5)*6

h²=144

h=12

(the negative solution of the root is ignored, bc h is some distance. distances are never negative)

let's plus 12 into line two, in the place of h. this will give us b

b*12/2=120

b*6=120

b=20

h=12 and b=20 are in the right ratio (note that both are multiples of 4, 12=4*3 and 20=4*5)

and 12*20/2 = 120

everything works out just nicely