SOLUTION: A triangle has vertices at (0,0), (3,3), and (-4,4). Classify the triangle by angles. What is the area of the triangle? What is the length of the longest side of the triangle?

Algebra ->  Triangles -> SOLUTION: A triangle has vertices at (0,0), (3,3), and (-4,4). Classify the triangle by angles. What is the area of the triangle? What is the length of the longest side of the triangle?       Log On


   

Question 1022845: A triangle has vertices at (0,0), (3,3), and (-4,4). Classify the triangle by angles. What is the area of the triangle? What is the length of the longest side of the triangle? What is the perimeter of the triangle?
Answer by ikleyn(52781) About Me  (Show Source):
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A triangle has vertices at (0,0), (3,3), and (-4,4). Classify the triangle by angles. What is the area of the triangle?
What is the length of the longest side of the triangle? What is the perimeter of the triangle?
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It is right-angled triangle.

One leg lies in the (+45°) straight line y = x and has the length 3%2Asqrt%282%29.

The other leg lies in the (+135°) straight line y = -x and has the length 4%2Asqrt%282%29.

This right-angled triangle has the legs ratio 3%2F4, hence, it is 3:4:5 right-angled triangle. 

It implies that the hypotenuse has the length 5%2Asqrt%282%29.

The area is %281%2F2%29%2A%283%2Asqrt%282%29%29%2A%284%2Asqrt%282%29%29 = 3*4 = 12 square units.

The perimeter is %283%2B4%2B5%29%2Asqrt%282%29 = 12%2Asqrt%282%29 units.