Final answer:
The simplified expression for the perimeter of the irregular quadrilateral with given side lengths is (39/4)t - 1. We obtain this by adding all side lengths and combining like terms.
Step-by-step explanation:
To find the perimeter of an irregular quadrilateral with side lengths (2 1/4t - 5), (4t + 3), (1/2t - 1), and (3t + 2), we simply add together the lengths of all four sides. The perimeter (P) is given by the expression:
P = (2 1/4t - 5) + (4t + 3) + (1/2t - 1) + (3t + 2)
To simplify the expression, we first convert the mixed number 2 1/4t to an improper fraction, which is (9/4)t. The simplified expression will be a combination of all the t terms and the constant terms. We perform the addition by combining like terms:
P = (9/4)t + (4t) + (1/2t) + (3t) - 5 + 3 - 1 + 2
We then convert all the coefficients of t to have the same denominator, which in this case is 4, to combine them:
P = (9/4)t + (16/4)t + (2/4)t + (12/4)t + (-1)
Now, add the coefficients of t:
P = ((9 + 16 + 2 + 12)/4)t - 1
P = (39/4)t - 1
And this is the simplified expression for the perimeter of the quadrilateral.