How do you answer this

Question

asked Aug 16, 2019 75.6k views

1 Answer

Shamim Ahmmed · Answer 1 · 2019-08-20T21:20:37+0000

I'm going to guess the question is determine the perimeter and area of a triangle SBA, S(15,-8), B(-2,21), A(0.0).

When we have a triangle with one vertex on the origin, the signed area is half the cross product of the other two vertices:

Area = (1/2) | 15(21) - (-8)(-2) | = (1/2)(299) = 149.5

It seems silly to round this exact answer, but we do what we're told.

Answer: Area=150

The perimeter P is the sum of the lengths of the three sides, so we use the distance formula three times. 8,15,17 is a known Pythagorean Triple.

P=√((15 - -2)^2 + (-8 - 21)^2) + √((-2)^2 + 21^2) + √(15^2 + (-8)^2)

P = √(1130) + √(445) +17

$P \approx 71.71$

Answer: Perimeter=72