Question

The base of a triangle is (4x) m, and the height is (2x + 5) m. Findthe area of the triangle in terms of the variable x

Answer 1

As given by the question

There are given that the base of the triangle is (4x) and the height is (2x+5).

Now,

From the formula of area of a triangle;

$\text{Area of triangle=}\frac{\text{1}}{2}\times base\times height$

Then,

Put the both value into the above formula

So,

$\begin{gathered} \text{Area of triangle=}\frac{\text{1}}{2}\times base\times height \\ \text{Area of triangle=}\frac{\text{1}}{2}\times4x\times(2x+5) \\ \text{Area of triangle=}\frac{\text{1}}{2}\times4x(2x+5) \end{gathered}$

Then,

$\begin{gathered} \text{Area of triangle=}\frac{\text{1}}{2}\times4x(2x+5) \\ \text{Area of triangle=}\frac{\text{1}}{2}\times(8x^2+20x) \\ \text{Area of triangle=}\frac{(8x^2+20x)}{2} \\ \text{Area of triangle=}4x^2+10x \end{gathered}$

Hence, the area of a triangle is shown below:

$\text{Area of triangle=4x}^2+10x$