Questions: Write a simplified expression that represents the perimeter of an irregular quadrilateral with side lengths (2 1/4 t-5), (4 t+3), (1/2 t-1), and (3 t+2).

Solution Steps

The side lengths of the irregular quadrilateral are given as:

• $\text{side1} = 2 \frac{1}{4} t - 5 = \frac{9}{4} t - 5$
• $\text{side2} = 4t + 3$
• $\text{side3} = \frac{1}{2} t - 1$
• $\text{side4} = 3t + 2$

To find the perimeter $P$, we sum all the side lengths: $$P = \left( \frac{9}{4} t - 5 \right) + (4t + 3) + \left( \frac{1}{2} t - 1 \right) + (3t + 2)$$

Combining like terms, we simplify the expression for the perimeter: $$P = \left( \frac{9}{4} t + 4t + \frac{1}{2} t + 3t \right) + (-5 + 3 - 1 + 2)$$ This results in: $$P = \frac{39}{4} t - 1$$ Thus, the simplified expression for the perimeter of the irregular quadrilateral is: $$P = \frac{39}{4} t - 1$$

Final Answer