Question

The height of a triangle is 6 cm longer than its base. If its area is 36 square cm, what is the length of the base and the height?

Answer 1

Given:

There are given that the height of a triangle is 6 cm longer than its base.

Explanation:

According to the question.

We need to find the length of the base and the height.

So,

Suppose the height of the triangle is H and the base of the triangle

According to the given data:

$H=B+6$

Then,

From the area of the triangle:

$A=\frac{1}{2}(B\times H)$

Then,

Put all the value into the give formula:

So,

$\begin{gathered} A=\frac{1}{2}(B\times H) \\ 36\times2=\frac{1}{2}\times2\times B(B+6) \\ B^2+6B=72 \end{gathered}$

Then,

$\begin{gathered} B^{2}+6B=72 \\ B^2+6B-72=72-72 \\ B^2+6B-72=0 \end{gathered}$

Then,

$\begin{gathered} B^{2}+6B-72=0 \\ (B+12)(B-6)=0 \\ B=-12;B=6 \end{gathered}$

Then,

According to the concept, the value of the base cannot be negative.

So,

The value of the base is:

$B=6$

Now,

From the give statement:

$\begin{gathered} H=B+6 \\ H=6+6 \\ H=12 \end{gathered}$

Final answer:

Hence, the base of the triangle is 6 and the height of the triangle is 12.