Problema Solution
The area of a rectangle is 32, and its perimeter is 24 . Find its dimensions and diagonal.
Longer side:
Shorter side:
Diagonal:
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Solution:
x = longer side
y = shorter side
z = diagonal
xy = 32
y = 32/x
2x + 2y = 24
2x + 2(32/x) = 24
2x^2 + 64 = 24x
x^2 - 12x + 32 = 0
(x-8)(x-4) = 0
x = 8
x = 4
Since x = longer, x = 8
y = 32/8
y = 4
z = sqrt(x^2+y^2)
z = sqrt(8^2 + 4^2)
z = 4 sqrt(5)
Longer side: 8
Shorter side: 4
Diagonal: 4 sqrt(5)