SOLUTION: The perimeter of a regular lawn is 60m and its diagonal is 25m. If the length of the lawn is {{{ x }}}m, show that {{{ 2x^2-60x+275=0 }}}. How to solve this question? Thanks.

Question 924438: The perimeter of a regular lawn is 60m and its diagonal is 25m. If the length of the lawn is m, show that .
How to solve this question? Thanks.
Answer by Cromlix(4381) (Show Source): You can put this solution on YOUR website!
Perimeter = 2 x Length + 2 x width
Length = x
Width = y
Perimeter = 2x + 2y
2x + 2y = 60
2y = 60 - 2x
2y = 2(30 - x)
Divide both sides by 2
y = 30 - x
Using the diagonal.
x^2 + y^2 = 25^2 (Pythagoras theorem)
Substitute y = 30 - x
x^2 + (30 - x)^2 = 625
Multiply out bracket
x^2 + 900 - 60 x + x^2 = 625
Collect like terms
2x^2 - 60x + 900 - 625 = 0
2x^2 - 60x + 275 = 0
Your answer.
Hope this helps.
:-)
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