Question

30 POINTS, Im pretty hopeless at this point and i know someone is just gonna rob the points thanks anyways

Answer 1

Answer:

$\dfrac{ah}{a+h}$

Step-by-step explanation:

Consider similar triangles BMC and KMN.

In these triangles,

$\dfrac{BC}{KN}=\dfrac{MO}{MP},$

where O is the point of intersection of BC and MP.

Note that segment OP has the length the same as the side of the square ABCD. Hence,

$\dfrac{BC}{a}=\dfrac{h-BC}{h},\\ \\BC\cdot h=a(h-BC),\\ \\BCh=ah-aBC,\\ \\BC(h+a)=ah,\\ \\BC=\dfrac{ah}{a+h}.$