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Caas
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A rectangular photograph of diagonal 12 cm is enlarged 04 Jun 2007, 13:13
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A rectangular photograph of diagonal 12 cm is enlarged according to the principle of similarity of 2 rectangles. The diagonal of the enlarged photo -15 cm. Find the percentage of increase in the area of the photograph.



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Dek
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A rectangular photograph of diagonal 12 cm is enlarged 04 Jun 2007, 13:46
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I'm getting approx 50%.
Did some logic math.

If the diagonal is 15, since its right angled, the sides could be 9 and 12
(multiple of the 3-4-5 right angled triangle.)
So area = 12*9= 108

When diagonal is 12 - I assumed sides to be closest to 8 and 9
since 8^2 + 9^2 = 145
Initial area = 8*9 = 72

Diff = (108-72)/72 * 100
= 50
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galt
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A rectangular photograph of diagonal 12 cm is enlarged 04 Jun 2007, 15:39
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Original rectangle measurements: length = L, Width = rL (where r is some constant)
New rectangle measurements: length = M, Width = rM (the ratio will stay the same, since thats the definition of similar rectangles)

144 = L^2 + (rL)^2 = (1+r^2) * L^2
225 = M^2 + (rM)^2 = (1+r^2) * M^2

New Area = M * rM
Old Area = L * rL

Ratio = (M * rM) / (L * rL) = M^2/L^2 = 225/144

Therefore % increase = (225 - 144)/144 = 81/144 %
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plaguerabbit
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A rectangular photograph of diagonal 12 cm is enlarged 04 Jun 2007, 19:29
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Quick guesstimation based on Dek's reasoning but where I actually calculated the edges gives me...

64%?
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Caas
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A rectangular photograph of diagonal 12 cm is enlarged 06 Jun 2007, 07:36
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Dek is right
answer is 56,25 %

15^2/12^2 = Area new / Area old
Deduct 1 and multiply be 100 both parts
(225-144)*100/144 = 100*(Area new - Area old)/Area old
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saurster
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A rectangular photograph of diagonal 12 cm is enlarged 06 Jun 2007, 08:16
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yes, the answer indeed comes to (81/144)*100. If you want a more algebraic equation based approach;

Old rectangle; sides are x, y, diag = 12
new rectangle; sides are x', y', diag = 15
From the question stem, since the rectangles are enlarged by similar rectangle ratios then;
x'/x = y'/y = 15/12

Area of old rect. = xy
Area of new rect = x'y'

therefore, percentage increase = ((x'y' - xy)/xy)*100
simplifying this we get (x'y'/xy - 1)*100
= (((x'/y')*(x/y))-1)*100 = ((15/12*15/12) -1)*100 = 81/144*100
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A rectangular photograph of diagonal 12 cm is enlarged 06 Jun 2007, 16:03
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(81/144) * 100 is purrrfect :)



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