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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...
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April 16th, 2016, 02:56 PM   #2
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Let d=length of diagonal. $\displaystyle d^2=2(x^2+y^2)=2\times 50$

Therefore d=10.
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April 16th, 2016, 10:41 PM   #3
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Thanks so much mathman
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