The shorter side of a rectangle is 20 m. Decreasing the longer side by 30 cm reduces the perimeter by one half. How long are the longer sides of the original rectangle? Explain the reasoning.
Let S = shorter side, L = longer side and P = perimeter (all in meters).
2S + 2L = P ---> 40 + 2L = P
2S + 2(L - .3) = P/2 ---> 40 + 2(L - .3) = P/2
Substitute the value for P from the first equation into the second. Solve for L.
I hope this helps. Thanks for asking.
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To solve this problem, we need to use the given information about the shorter side and the perimeter reduction.
Let's start by finding the original longer side length:
1. We know that the shorter side is 20m, but the length of the longer side is unknown. Let's call the longer side length "L" (in meters).
2. If we decrease the longer side by 30 cm, which is equal to 0.3m, the new longer side length becomes L - 0.3.
3. The new rectangle with the shortened longer side has a perimeter that is one-half of the original perimeter. Therefore, we can set up an equation using the perimeter formula:
Original perimeter = 2 * (shorter side + longer side)
New perimeter = 2 * (shorter side + new longer side)
Since the new perimeter is one-half of the original perimeter, we can write:
2 * (shorter side + new longer side) = 0.5 * (2 * (shorter side + longer side))
2 * (20 + L - 0.3) = 0.5 * (2 * (20 + L))
4. Simplifying the equation:
40 + 2L - 0.6 = 20 + 0.5L
5. Rearranging the equation:
1.5L - 0.5L = 20 - 40 + 0.6
1L = -20 + 0.6
1L = -19.4
Since a negative length doesn't make sense in this context, we can conclude that there is no valid solution for the longer side length of the original rectangle.