My Math Forum Finding the length of the diagonal of a rectangle?

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April 16th, 2016, 02:20 PM   #1
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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...
Attached Images
 Screen Shot 2016-04-16 at 23.06.44.jpg (14.5 KB, 6 views)

 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. Thanks from mathsmansion
 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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