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1. Question : The perimeter of a rectangle is 34cm. Given that the diagonal is of length 13cm, and that the width is xcm, derive the equation x^2 -17x +60 =0.
Hench find the dimensions of the rectangle. Any help would be greatly appreciated, thanks.
2. (Original post by redmcq)
Question : The perimeter of a rectangle is 34cm. Given that the diagonal is of length 13cm, and that the width is xcm, derive the equation x^2 -17x +60 =0.
Hench find the dimensions of the rectangle. Any help would be greatly appreciated, thanks.
Simultaneous equations
Let x and y be the two sides and form 2 equations
3. (Original post by ODES_PDES)
Simultaneous equations
Let x and y be the two sides and form 2 equations
i've tried this, managed to form 2x+2y=34 but dont know how to form other equation? i tried using pythagoras with the hypotenuse = 13 and rearranged to get 13-x=y but still cant find solution.
4. one side of the rectangle = x

the other is ( 34 - 2x ) / 2

now do pythagoras with the diagonal of 13
5. (Original post by redmcq)
Question : The perimeter of a rectangle is 34cm. Given that the diagonal is of length 13cm, and that the width is xcm, derive the equation x^2 -17x +60 =0.Hench find the dimensions of the rectangle. Any help would be greatly appreciated, thanks.

*I have put the solutions in spoilers, so only look when you have to *

2x + 2y = 34 can be simplified to x + y = 17

you can also work out y in terms of x using pythagoras' theorem:
Spoiler:
Show
a^2 + b^2 = c^2
x^2 + y^2 = 169
y^2 = 169 - x^2
y = root(169 - x^2)
since you have the value for y, in terms of x, you can substitute this back into your original equation and play around with it until you get the equation given in the question
Spoiler:
Show

X + root(169-x^2) = 17

Root(169-x^2) = 17 - x

169 - x^2 = (17 - x)(17 - x)

169 - x^2 = 289 - 34x + x^2

-x^2 = 120 - 34x + x^2

2x^2 + 120 - 34x = 0

x^2 -17x + 60 = 0

From here, I am assuming you know how to work out the value of x:
Spoiler:
Show
use the quadratic formula - you will have two possible outcomes.
remember that dimensions can only be positive
6. Thanks guys!

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