Question

The figure below shows square ABCD inscribed on square PQRM on a coordinate plane. Which of the following expressions represents the perimeter of triangle BRC in units?
A.4
B.6
C.2√5
D.6 + 2√5

Answer 1

The hypotenuse of the triangle is given by:
 $CB ^ 2 = RC ^ 2 + RB ^ 2$
 Substituting values:
 $CB ^ 2 = 2 ^ 2 + 4 ^ 2$
 Clearing CB we have:
 $CB = \sqrt{ 2 ^ 2 + 4 ^ 2} CB = \sqrt{ 4 + 16} CB = \sqrt{20} CB = \sqrt{4*5} CB = 2\sqrt{5}$
 Then, the perimeter of the triangle is:
 $P = RB + RC + CB$
 Substituting values:
 $P = 4 + 2 + 2 \sqrt{5} P = 6 + 2 \sqrt{5}$
 Answer:
 the perimeter of triangle BRC in units is:
 D.6 + 2√5

Answer 2

d...........................................................................