Question 772210: I am having tremendous amounts of trouble on these geometry word problems from my summer packet. I keep trying to use formulas to figure out the answers but it seems i cant quiet put them together correctly
q: The second side of a triangle is four more than the first side, the third side is five more than the second. If the product of the first and third side is added to the product of the second and third sides, the result is 124 more than twice the square of the first side. find the perimeter to the triangle.
a=1st side b=second c=third
i was able to figure out the a+4=b and a+9=c or b+5=c
a(a+9) +( (a+4)+(a+9)) =124 but then what? this is where i got stuck.
thank you
Answer by John10(297)   (Show Source):
You can put this solution on YOUR website! Q: The second side of a triangle is four more than the first side, the third side is five more than the second. If the product of the first and third side is added to the product of the second and third sides, the result is 124 more than twice the square of the first side. Find the perimeter to the triangle.
a=1st side b=second c=third
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Translation:
b = a + 4
c = b + 5
ac + bc = 124 + 2a^2
Find a, b, and c = ?
For this problem, I recommend that you write b and c in term of a then you substitute into equation ac + bc = 124 + 2a^2.
You know b = a + 4
c = b + 5 = (a + 4) + 5 = a + 9
So
b = a + 4 and c = a + 9
Substitute into the last equation
a(a + 9) + (a + 4)(a + 9) = 124 + 2a^2
a^2 + 9a + a^2 + 13a + 36 = 124 + 2a^2
2a^2 + 22a + 36 = 124 + 2a^2
22a = 88
a = 88/22
a = 4
If a = 4 then
b = a + 4 = 4 + 4 = 8
c = a + 9 = 4 + 9 = 13
The perimeter of triangle = a + b + c = 4 + 8 + 13 = 25
Hope it helps you!
John10 (john100185@yahoo.com)
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