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What are the dimensions of a rectangle when one side is 1.5 cm longer than the other side and its area in numerical terms is the same as its perimeter?
l = w + 1.5
p = 2(l + w) = 4w + 3
a = lw = w2 + 1.5w
w2 + 1.5w = 4w + 3
2w2 + 3w = 8w + 6
2w2 - 5w - 6 = 0
Quadratic formula gives w = 3.38 so l = 4.88, making a = 16.49
P = 2 (3.38 + 4.38) = 16.52. Near enough for Wiki!
Improved Answer:
Let the length be (x+1.5) and the width be x:
length*width = 2(length+width)
(x+1.5)*x = 2(x+1.5+x)
x2+1.5x = 4x+3
x2+1.5x-4x-3 = 0
x2-2.5x-3 = 0
Solving the above quadratic equation gives a positive value of 3.386000936 for x.
Therefore: length = 4.886000936 cm and width = 3.386000936 cm
Check: length*width = 16.54400374 cm2 and 2(length+width) = 16.54400374 cm
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i don't know what length of rectangle is 7 cm longer than the width the perimeter of the rectangle is 46 cm .what is the length of the of the rectangle ?
