Question

The road from A to E and the road from C and D are perpendicular and intersect at point F. Theresa's house is at C, 500 feet from the intersection. Ray's house is at D, 750 feet from the intersection. Ivy's house is at E, 750 feet from the intersection.

Zanas house is at A, 500 feet from the intersection, and Tan's house is at B, 750 feet from F. Which distance is longer, the distance from Zana's house to Tan's house or the distance from Theresa's house to Is house? Show how you know.

Answer 1

Explanation:

what is meant by "distance" ?

ground distance (using the roads to get there), or air distance (line of sight) ?

I have to assume we mean air distance, as the ground distance is the same in both cases (500 ft + 750 ft = 1250 ft).

for the air distance we need to use Pythagoras

c² = a² + b²

with c being the Hypotenuse (the side opposite of the 90° angle), and a and b being the legs.

Zana to Tan = AB

FB² = FA² + AB²

750² = 500² + AB²

562,500 = 250,000 + AB²

312,500 = AB²

AB = 559.0169944... ft

Theresa to Ivy = CE

CE² = CF² + FE²

CE² = 500² + 750² = 250,000 + 562,500 =

= 812,500

CE = 901.3878189...

so, the distance from Theresa to Ivy is longer.