Answers:
- x = 1031/55 = 18.74545 approximately
- area = 35,542.92 square units approximately
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Explanation:
The perimeter is the sum of the exterior sides. We'll add up these three sides
and set the sum equal to the perimeter 1013
The equation we need to solve is
(16x+27)+(14x-45)+(25x) = 1013
Solving for x leads to...
(16x+27)+(14x-45)+(25x) = 1013
16x+27+14x-45+25x = 1013
(16x+14x+25x)+(27-45) = 1013
55x-18 = 1013
55x = 1013+18
55x = 1031
x = 1031/55
x = 18.74545 approximately
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Use this x value to find the length of each side. I'll use the decimal form of x. We get the following side lengths:
- 16x+27 = 16*(18.74545) + 27 = 326.9272
- 14x - 45 = 14*(18.74545) - 45 = 217.4363
- 25x = 25*(18.74545) = 468.63625
Those values are approximate.
We can then find the area of the triangle
area = (1/2)*base*height
area = (1/2)*(326.9272)*(217.4363)
area = 35,542.92036868
area = 35,542.92
The area is approximate as well.
