Question

Triangle PQR
has vertices P(0,0)
, Q(9.42,0)
, and R(6,2.4)
. Triangle PQS
has vertices P(0,0)
, Q(9.42,0)
, and S(5,y)
. The area of triangle PQS
is three times the area of triangle PQR
. Compute the value of y, the missing coordinate of vertex S
.

Answer 1

Base PQ lies on the x-axis, so the triangle areas are proportional to the heights (the y-coordinates) above that base. For R the height is 2.4, so for S the height must be 3·2.4 = 7.2.

Thus y = 7.2 (or y = −7.2 if you allow the triangle to lie below the base; usually the positive value 7.2 is intended).