Question 1208009: understand and solve the situation:new houses are being constructed in calle serye. the residents of this new housing project use a 17m long path that cuts diagonally across a vacant rectangular lot. before the diagonal lot was constructed, they had to walk a total of 23 m long along the two sides if they want to go from one corner to an opposite corner. write the quadratic equation that represents the problem if the shorter side is x. identify the values of a, b, and c.
Found 2 solutions by mananth, ikleyn:
Answer by mananth(16946)   (Show Source):
You can put this solution on YOUR website!
x^2+(23-x)^2 = 17^2 ( using Pythagoras theorem)
x^2 +529 -46x+x^2 = 289
2x^2 -46x -(529-289)=0
2x^2 -46x +240=0 is the required equation
comparing with ax^2+bx+c=0 we get
a=2, b=-46, c=240
 .
Corrected solution
Answer by ikleyn(52821)  (Show Source):
You can put this solution on YOUR website! .
understand and solve the situation:new houses are being constructed in calle serye.
the residents of this new housing project use a 17m long path that cuts diagonally
across a vacant rectangular lot. before the diagonal lot was constructed, they had to walk
a total of 23 m long along the two sides if they want to go from one corner to an opposite corner.
write the quadratic equation that represents the problem if the shorter side is x. identify the values of a, b, and c.
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The post by @mananth has arithmetic errors.
I came to bring a correct solution.
x^2 + (23-x)^2 = 17^2 ( using Pythagoras theorem)
x^2 + 529 - 46x + x^2 = 289
2x^2 - 46x + (529-289) = 0
2x^2 - 46x + 240 = 0 is the required equation
comparing with ax^2 + bx + c = 0, we get
a = 2, b = -46, c = 240
In the last equation, divide both sides by 2 (= reduce the common factor of 2)
comparing with x^2 - 23x + 120 = 0
a = 1, b = -23, c = 120
Factor left side
(x-8)*(x-15) = 0.
The roots are x = 8 and x = 15.
The shortest leg of the right-angled triangle is 8 units. ANSWER
Solved (with no errors)
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After seeing my post, @mananth fixed his final answer, and it is good.
But still remained small errors inside his post.
These errors also should be fixed.
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You may ask me why I worry so much about mistakes?
I am happy to answer this question.
According to statistics, each post at this forum is read on average
by more than 10 other visitors later. That's why I'm worried about.
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