Question

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

Answer 1

G

EXPLANATION :

Recall the area formula of a triangle :

`A=(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=(1)/(2)((36)/(x+y))((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=(1)/(2)((36)/(x+y))[((x+y)(x-y))/(12)] \\ \\ A=(1)/(2)(\frac{36}{\cancel{x+y}})[\frac{\cancel{(x+y)}(x-y)}{12}] \\ \\ A=(1)/(2)(36)((x-y)/(12)) \\ \\ A=(3)/(2)(x-y) \end{gathered}`