Question 970: A piece of wire 38m long is bent into the shape of a rectangle that is twice as long as it is wide . Find its dimensions.
Answer by veeru(1)   (Show Source):
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A piece of wire is bent into shape of rectangle. So, length of the wire is same as the perimeter of rectangle.
Recall that the perimeter of a figure is the sum of the measures of its sides.
Let the length of the rectangle be L and the width be W.
The sum of the measures of the sides of rectangle is: L + W + L + W
= 2L + 2W
= 2(L + W)
But the perimeter of the rectangle is 38m.
So, 2(L + W) = 38. -------- Equation (1)
Also given that the length is twice the width.
So, L = 2W. -------- Equation (2)
Substitute the equation 2 in equation 1:
2(2W + W) = 38
2(3W) = 38
6W = 38
Divide by 6 on both sides:
W is approximately equal to 6.33.
Substitute 6.33 for W in the equation 2:
L = 2(6.33)
=12.66
L is approximately equal to 12.66.
So, the approximate dimensions of the rectangle are 6.33m and 12.66m.
The final answer can also be expressed as fractions: 17/3 and 38/3
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