SOLUTION: ABC is a triangle with sides a, b, and c, as shown in the diagram. If angle C = 90 degrees, c = 4, and a + b = the square root of 18, then the area of the triangle is... A)1/2 B)1
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-> SOLUTION: ABC is a triangle with sides a, b, and c, as shown in the diagram. If angle C = 90 degrees, c = 4, and a + b = the square root of 18, then the area of the triangle is... A)1/2 B)1
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Question 665289: ABC is a triangle with sides a, b, and c, as shown in the diagram. If angle C = 90 degrees, c = 4, and a + b = the square root of 18, then the area of the triangle is... A)1/2 B)1 C)2 D)4 E)18 Answer by Edwin McCravy(20055) (Show Source):
You can put this solution on YOUR website! ABC is a triangle with sides a, b, and c, as shown in the diagram. If angle C = 90 degrees, c = 4, and a + b = the square root of 18, then the area of the triangle is... A)1/2 B)1 C)2 D)4 E)18
Since a + b = Ö18, b = Ö18 - a.
The area is A = ab = a(Ö18 - a)
By the Pythagorean theorem:
a² + b² = c²
a² + (Ö18 - a)² = 4²
a² + 18 - 2aÖ18 + a² = 16
2a² - 2aÖ18 = -2
Divide through by 2
a² - aÖ18 = -1
Multiply through by -1
-a² + aÖ18 = +1
aÖ18 - a² = 1
Factor out a on the left:
a(a - Ö18) = 1
Notice that the area above is A = a(Ö18 - a), which just
happens to be the left side multiplied by . So let's
multiplty both sides of that equation through by :
a(a - Ö18) = ·1
So Area = a(a - Ö18) =
Answer:
Edwin
