Bunuel wrote:

In the figure above, what is the perimeter of ∆ ABC in terms of m?

(A) 10m

(B) 15m

(C) 17m

(D) 7m + 3√2 m

(E) 12m + 3√2 m

Attachment:

2017-08-13_0320.png

Let X be the point where B intersects side AC

Left triangle ABX is right isosceles (45-45-90) with side ratio \(x: x: x\sqrt{2}\)

3m corresponds with x

Hypotenuse, side AB, therefore is 3\(\sqrt{2}\)m

Triangle BCX, on the right, is 3-4-5 triangle. Hypotenuse, side BC, is 5m

Perimeter = sum of three side lengths

5m + 7m + 3\(\sqrt{2}\)m =

12m + 3\(\sqrt{2}\)m

Answer E

_________________

In the depths of winter, I finally learned

that within me there lay an invincible summer.

-- Albert Camus, "Return to Tipasa"