SOLUTION: The diagonal of a rectangle is 8 cm. The length of the rectangle is 1.6 cm more than the width. Find the dimmensions of the rectangle.

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Question 302231: The diagonal of a rectangle is 8 cm. The length of the rectangle is 1.6 cm more than the width. Find the dimmensions of the rectangle.
Answer by london maths tutor(243) About Me  (Show Source):
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Cutting the rectangle into half diagonally, it is a right angle triangle.
Using Pythagoras' Theorem: Length^2 + width^2 = Diagonal^2
Let's length = L , width = w and Diagonal = d
L = (w + 1.6)cm and d = 8cm
This gives:
%28w%2B1.6%29%5E2+%2B+w%5E2+=+8%5E2
%28w%2B1.6%29%5E2+%2B+w%5E2+=+64
%28w%5E2+%2B+2%281.6%29w+%2B+%281.6%29%5E2%29+%2B+w%5E2+=+64
2w%5E2+%2B+3.2w+%2B+2.56+-+64+=+0+

2w%5E2+%2B+3.2w+-+61.44+=+0+
Using w+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+ where
a = 2 , b = 3.2 and c = -61.44
w = 4.8 cm or - 6.4 (N/A)
and therefore, L = 4.8 + 1.6 = 6.4 cm
Answer: width = 4.8 cm and Length = 6.4 cm