The flat triangular lot depicted above is available for development. If X + X/2 = 150 meters, what is the area of the lot in square meters?
$$A.\ 125$$
$$B.\ 150\sqrt{3}$$
$$C.\ 1,500$$
$$D.\ 1,250\sqrt{3}$$
$$E.\ 2,500\sqrt{3}$$
The OA is D.
If X + X/2 = 150 then, X = 100. Now, we need to calculate the base of triangular lot,
$$100^2=50^2+b^2,\ then,\ b=\sqrt{100^2-50^2}=\sqrt{7500}=50\sqrt{3}$$
Now we can determine the area of the lot of the following way,
$$A_{\triangle}=\frac{1}{2}b\cdot h=\frac{1}{2}\left(50\sqrt{3}\right)\left(50\right)=1,250\sqrt{3}square\ meters$$
Is there a strategic approach to this PS question? Can any experts help, please? Thanks!
