13. The perimeter of the given rectangle is $50 \mathrm{~cm}$. Determine the length of each side of the rectangle.
\[
3 x-1
\]
\[
4 x+5
\]

Answer

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Answer

$\boxed{\text{Final Answer: The length of each side of the rectangle is 8 cm and 17 cm.}}$

Steps

Step 1 ：Let the length of the rectangle be $L = 3x - 1$ and the width be $W = 4x + 5$. We are given that the perimeter $P = 50$ cm.

Step 2 ：Using the formula for the perimeter of a rectangle, $P = 2(L + W)$, we can plug in the given values and solve for x:

Step 3 ：$50 = 2((3x - 1) + (4x + 5))$

Step 4 ：Solve for x:

Step 5 ：$x = 3$

Step 6 ：Substitute the value of x back into the expressions for L and W:

Step 7 ：$L = 3(3) - 1 = 8$

Step 8 ：$W = 4(3) + 5 = 17$

Step 9 ：$\boxed{\text{Final Answer: The length of each side of the rectangle is 8 cm and 17 cm.}}$