Question

The formula for the area of a triangle is A=1/2 bc where b is the length of the base and h is the height find the height of a triangle that has an area of 30 square unties and a base measuring 12 units

A-3 units
B-5 units
C-8units
D-9 units

Answer 1

We can see from the question that we have the following information:

• The area of a triangle is given by:

`A_(triangle)=(bh)/(2)`

• The area of the triangle, in this case, is 30 square units (30u²).

,

• The base, b, of the triangle is 12 units (12u).

And we need to find the height of the triangle, h.

1. To find the height of the triangle, we already have the area (30 square units), and the base of the triangle (12 units).

2. Then we have to substitute these values into the general formula for the area of a triangle, and then solve for the height of the triangle as follows:

`\begin{gathered} A_(triangle)=(bh)/(2) \\ \\ 30u^2=((12u)h)/(2) \end{gathered}`

Notice that u represents units (it could be yards, meters, centimeters, and so on).

3. To solve for h, we can proceed as follows:

Multiply by 2 to both sides of the equation:

`\begin{gathered} 2(30u^2)=2((12u)h)/(2)\Rightarrow(2)/(2)=1,(a)/(a)=1 \\ \\ 60u^2=(12u)h \end{gathered}`

Divide both sides of the equation by 12u:

`\begin{gathered} (60u^2)/(12u)=(12u)/(12u)h\Rightarrow(12u)/(12u)=1 \\ \\ (60u^2)/(12u)=h \\ \\ (60)/(12)=5,(u^2)/(u)=u\text{ Then we have:} \\ \\ 5u=h \\ \\ h=5u \end{gathered}`

Hence the measure of the base is 5u (5 units).

Therefore, in summary, we have that the height, h, of a triangle that has an area of 30 square units and a base measuring 12 units is 5 units (option B).