If the perimeter of rectangle is 68cm if the diagonal is 26cm find dimensions

perimeter = 2 (a + b), where a = length and b = width

p = 68

a+b = 34

so

a = 34-b

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diagonal = c = 26 cm

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Pythagorean Theorem teaches us that:

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c^2 = a^2 + b^2

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Substitute for a = 34-b and c = 26

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26^2 = (34-b) ^2 + b^2

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Collect terms.

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676 = (b^2 - 68b + 1156) + b^2

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2b^2 - 68b + 480 = 0

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b^2 - 34b + 240 = 0