A rectangle has a perimeter of 32 and an area of 56. Find the length of its diagonal.
+37146 2 l + 2w = 32
l * w = 56 l = 56/w
Sub second into first equation
112/w + 2w = 32 multiply by w
2w^2 - 32w + 112 = 0 Quadratic formula shows w = 8+ 2 sqrt 2 then l = 8-2sqrt2
d^2 = (8+ 2 sqrt2)^2 + (8-2 sqrt2)^2
d^2 = 144 d = 12
+1252 Another similar way as EP
Width = x, Height = y
2x+2y=32
xy=56
So x+y=16
Square it
x^2+y^2+2xy=256
Plug in xy=56
x^2+y^2=144
Diagonal is sqrt of that, so 12.
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