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Lebar persegi panjang adalah sepertiga dari panjang nya. Jika keliling persegi panjang tersebut $56\,\text{cm}$ . Berapakah luas persegi panjang tersebut?

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Evaluate rational exponents

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Q. Lebar persegi panjang adalah sepertiga dari panjang nya. Jika keliling persegi panjang tersebut

56\,\text{cm}

. Berapakah luas persegi panjang tersebut?

Define Variables: Let's call the length of the rectangle $L$ and the width $W$ . We know that $W = \frac{L}{3}$ and the perimeter $P = 2L + 2W = 56\,\text{cm}$ .
Express Width in Terms of Length: First, let's express $W$ in terms of $L$ : $W = \frac{L}{3}$ .
Plug Width into Perimeter Formula: Now, let's plug $W$ into the perimeter formula: $P = 2L + 2\left(\frac{L}{3}\right) = 56$ .
Simplify Equation: Simplify the equation: $2L + \frac{2L}{3} = 56$ .
Multiply to Eliminate Fraction: Multiply everything by $3$ to get rid of the fraction: $6L + 2L = 168$ .
Combine Like Terms: Combine like terms: $8L = 168$ .
Find Length: Divide both sides by $8$ to find $L$ : $L = \frac{168}{8} = 21$ cm.
Find Width: Now we can find $W$ using $W = \frac{L}{3}$ : $W = \frac{21}{3} = 7$ cm.
Calculate Area: Finally, calculate the area $A$ of the rectangle using $A = L \times W$ : $A = 21 \times 7 = 147 \text{ cm}^2$ .

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