Question

I need help figuring out which expression can be used to represent the area of the triangle

Answer 1

ANSWER :

G

EXPLANATION :

Recall the area formula of a triangle :

$A=\frac{1}{2}bh$

From the problem, the base is 36/(x + y) and the height is (x^2 - y^2)/12

Using the formula above :

$\begin{gathered} A=\frac{1}{2}(\frac{36}{x+y})(\frac{x^2-y^2}{12}) \\ \\ \text{ Note that }x^2-y^2\text{ is equal to }(x+y)(x-y) \\ \text{ That will be :} \\ A=\frac{1}{2}(\frac{36}{x+y})[\frac{(x+y)(x-y)}{12}] \\ \\ A=\frac{1}{2}(\frac{36}{\cancel{x+y}})[\frac{\cancel{(x+y)}(x-y)}{12}] \\ \\ A=\frac{1}{2}(36)(\frac{x-y}{12}) \\ \\ A=\frac{3}{2}(x-y) \end{gathered}$