Question

If the triangle has a base length of 9cm and a total area of 27 cm what is the height?

Answer 1

Answer: The height of the triangle is 6cm.

Step-by-step explanation: So, the general formula to finding the area of the triangle is as follows....

`bh/2= a`. This equation means, base (b) multiplied by height (h), divided by 2, which equals to the area of the triangle.

You may ask, why two? Because two triangles make a rectangle ( you can cut a rectangle, then cut it diagonally, you will get two identical triangles. So that is the reason you divide it by two, here it is 6; 3 is not an answer because the area is 27cm, which most peers make mistake in.

To prove this, here is the algebraic way to deal with this:

`bh/2=a` , we can replace these letters, we can replace "b" with 9 and "a" as 27. We are not replacing "h" as we have to figure it out. The equation now becomes :

`(9Xh)/2 = 27`

Now, we have to solve this for "a", we have to move all the digits to the other side except "h", to figure out the value of "h".

So, we multiply by 2 for both sides, as opposite of multiplication is division, to get rid of the 2.

So, the equation becomes :

`9Xh= 27X2\\\\9Xh= 54`

Now, we have to get rid of 9, we can simply do it, by, dividing by 9 on both sides.

`9Xh=54`

÷9. ÷9

Which becomes :

`h=54/9\\\\h= 6`

So our final answer is 6. Hope this helps!

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Answer 2

The height of the triangle is 6 cm.

Explanation:

The formula for the area of a triangle is

`A=(1)/(2) bh`

Note

`A` is the area of the triangle

`b` is the base of the triangle

`h` is the height of the triangle

In this example we are asked to evaluate the height.

Lets solve for
`h` in the formula below.

`A=(1)/(2) bh`

Move
`bh` into the numerator of the fraction.

`A=(bh)/(2)`

Multiply both sides of the equation by
`2`.

`2A=bh`

Divide both sides of the equation by
`b`.

`(2A)/(b)=h`

Now we have an equation to evaluate the height of the triangle.

`h=(2A)/(b)`

Numerical Evaluation

In this example we are given

`b=9\\A=27`

Substituting our values into the equation for height yields

`h=(2*27)/(9)`

Multiply
`2` by
`27`.

`h=(54)/(9)`

Divide
`54` by
`9`.

`h=6`