Question

For the following figure, the formula for the area A of a triangle is$A=\frac{1}{2}bh$ . Where b is the measure of the base and h is the measure of height. Write the area of the triangle when x=23.

Short answer

The solution is $A=364$.

Step-by-step solution

Step 1- Consider the figure.

Consider the figure.

Step 2- Step description.

Substitute the measure of height and base from the figure into the formula and simplify as follows:

$\begin{array}{l}A=\frac{1}{2}bh\\ A=\frac{1}{2}(x+3)(x+5)\\ A=\frac{1}{2}(x^2+8x+15)\end{array}$

Step 3- Step description.

Substitute 23 for x in the expression obtained.

$\begin{array}{l}A=\frac{1}{2}(x^2+8x+15)\\ A=\frac{1}{2}({23}^2+8\left(23\right)+15)\\ A=364\end{array}$

Therefore, the area is 364 square units.