Let's solve the problem step by step:

Step 1: Define variables

Let:

• $x$ be the length of the longer side of the rectangle.
• $y$ be the length of the shorter side of the rectangle.

Step 2: Set up the equations

According to the problem:

1. The shorter side $y$ is 26 cm less than $\frac{5}{6}$ of the longer side $x$: $y = \frac{5}{6}x - 26$

2. The perimeter of the rectangle is 124 cm: $2x + 2y = 124$ Simplifying this equation: $x + y = 62$

Step 3: Substitute and solve

Substituting $y = \frac{5}{6}x - 26$ into $x + y = 62$: $x + \left(\frac{5}{6}x - 26\right) = 62$ $x + \frac{5}{6}x - 26 = 62$ Combine like terms: $\frac{11}{6}x = 88$ Multiply both sides by $\frac{6}{11}$: $x = \frac{88 \cdot 6}{11} = 48$

Step 4: Find $y$

Substituting $x = 48$ back into $y = \frac{5}{6}x - 26$: $y = \frac{5}{6}(48) - 26$ $y = 40 - 26$ $y = 14$

Final Answer

The dimensions of the rectangle are:

• Longer side: $48$ cm
• Shorter side: $14$ cm

Would you like more details or have any questions?

5 Relative Questions

1. How do you verify the correctness of these measurements?
2. What would the area of this rectangle be?
3. How would the problem change if the perimeter was different?
4. How can we generalize this method for other rectangle problems?
5. What happens if the ratio between the sides is altered?

Tip

Always double-check your equations and substitute back to verify that your solution satisfies all given conditions.