Q15. - Algebra 2

Question

Find the area of the triangle shown.     

Step-by-Step Solution

Answer

The area $\left(\Delta \right)$  of given right angle triangle is $\frac{15x^2+25x}{2}{\text{ ft}}^2$ .

Step 1. Write down the given information.

The given triangle is shown below with its parameter.

Step 2. Concept used.

The area  $\left(\Delta \right)$ of right-angle triangle having base  $\left(b\right)$ and perpendicular height  $\left(h\right)$ is given by the formula:

 $\text{Area}\left(\Delta \right)=\frac{1}{2}bh\mathrm{....}\left(1\right)$

Step 3. Calculation.

The area  $\left(\Delta \right)$ of given right angle triangle is evaluated as:

$\begin{array}{c}\text{Area}\left(\Delta \right)=\frac{1}{2}bh\mathrm{....}\left(\text{From }\left(1\right)\right)\\ =\frac{1}{2}(3x+5)\left(5x\right)\\ =\frac{15x^2+25x}{2}{\text{ ft}}^2\end{array}$

Step 4. Conclusion.

The area $\left(\Delta \right)$  of given right angle triangle is$\frac{15x^2+25x}{2}{\text{ ft}}^2$  .