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Can someone please help me out with this maths question please??

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.
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
Reply 2
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.
one side of the rectangle = x

the other is ( 34 - 2x ) / 2

now do pythagoras with the diagonal of 13
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 :smile:*

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

you can also work out y in terms of x using pythagoras' theorem:

Spoiler

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 :smile:

Spoiler


From here, I am assuming you know how to work out the value of x:

Spoiler

Reply 5
Thanks guys! :smile:

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