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April 16th, 2016, 02:20 PM  #1 
Newbie Joined: Mar 2016 From: London Posts: 21 Thanks: 0  Finding the length of the diagonal of a rectangle?
In the diagram shown (see attached) a rectangle is drawn inside a square in such a way that the four corners of the rectangle lie on the edges of the square. Each corner of the rectangle lies x cm from one corner of the square and y cm from another corner. a) Find an expression for the length of the diagonal of the rectangle in terms of x and y. b) Find an expression for the unshaded area in terms of x and y. c) Given that the unshaded area is 50 cm2, use (a) and (b) to find the length of the diagonal of the shaded rectangle. My attempt: SQRT means Square root of So for a) I did pythagoras a^2 + b^2 = c^2 to find the width of the shaded rectangle which I found to be SQRT2.x and to find the length of the shaded rectangle which I found to be SQRT2.y I then applied pythagoras a 3rd time to get 2.SQRT2 (x+y) b) I added all the unshaded areas to get x^2 + y^2 Can someone help me with c) please... 
April 16th, 2016, 02:56 PM  #2 
Global Moderator Joined: May 2007 Posts: 6,756 Thanks: 696 
Let d=length of diagonal. $\displaystyle d^2=2(x^2+y^2)=2\times 50$ Therefore d=10. 
April 16th, 2016, 10:41 PM  #3 
Newbie Joined: Mar 2016 From: London Posts: 21 Thanks: 0 
Thanks so much mathman 

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