In the diagram above, BF is an altitude drawn to the base AC, and AC is the side of square ABDE. If BF = h and the area of triangle ABC equals Q, find the area of the square (shaded) in terms of h and Q.
A. hQ
B. q/h
C. 2*(Q/h)^2
D. 4*(Q/h)^2
E. 1/4*(Q/h)^2
The OA is D
I solve this question as follows,
We know that the area of a triangle is defined by
$$\triangle_{area}=\frac{1}{2}\cdot b\cdot h$$
We know the area of triangle ABC = Q, then
$$AC=b=\frac{2\cdot \triangle_{area}}{h}=\frac{2\cdot Q}{h}$$
Finally, the area of the square shaded will be,
$$Area_{square}=(AC)^2=\left(\frac{2\cdot Q}{h}\right)^2=4\cdot\left(\frac{Q}{h}\right)^2$$
Has anyone another approach to solve this PS question? Regards!
