Question

The base of a triangle one-third of the triangle's height. Find the area of the triangle as a function of the base.

Answer 1

Alright well we know...the area of a triangle is

\[\large A = \frac{1}{2}bh\]

If we know that the base...is 1/3 of the hieght...we know

\[\large b = \frac{1}{3}h\]

So if the 'b' = that...we can rewrite the first equation we have up there as

\[\large A = \frac{1}{2}(\frac{1}{3}h)h\]

Notice all we did was write in \(\large \frac{1}{3}h\) instead of the 'b' we had before

Answer 2

So what would i have to do next?

Answer 3

its multiple choice.

Answer 4

Lets see...what are the choices?

Answer 5

1. A=3/2 b^2
2. A=9/2 b^2
3. A=1/6 b^2
4. A=1/18 b^2

Answer 6

Oh they want to replace the hieght instead...alright...so lets start over lol

Answer 7

Area of triangle

\[\large A = \frac{1}{2}bh\]

The base is 1/3 the height....also meaning that the height is 3 times the base....so

\[\large h = 3b\]

If THAT is true...we can now replace 'h' in our original equation...with '3b'

\[\large A = \frac{1}{2}b(3b)\]

Now we simplify...

\[\large A = \frac{1}{2}(3b^2)\]
\[\large A = \frac{3}{2}b^2\]

Answer 8

thank you soooo much :*

Answer 9

Anytime ;)