Rectangle Side Value 9Fec4F

1. **State the problem:** We need to find the value of $t$ in rectangle PQRS where the sides are labeled as follows: - Side $SP = 7t - 72$ - Side $PQ = 3t$ - Side $RQ = 4t - 36$ 2. **Recall properties of a rectangle:** Opposite sides of a rectangle are equal in length. 3. **Set up equations:** Since $SP$ is opposite to $RQ$, we have: $$7t - 72 = 4t - 36$$ Also, $PQ$ is opposite to $SR$, but $SR$ is not given explicitly, so we focus on the first equation. 4. **Solve the equation:** $$7t - 72 = 4t - 36$$ Subtract $4t$ from both sides: $$7t - \cancel{4t} - 72 = \cancel{4t} - 36$$ $$3t - 72 = -36$$ Add $72$ to both sides: $$3t - 72 + 72 = -36 + 72$$ $$3t = 36$$ Divide both sides by $3$: $$\frac{3t}{\cancel{3}} = \frac{36}{\cancel{3}}$$ $$t = 12$$ 5. **Check the value:** - $SP = 7(12) - 72 = 84 - 72 = 12$ - $RQ = 4(12) - 36 = 48 - 36 = 12$ Both sides are equal, confirming $t=12$ is correct. **Final answer:** $$t = 12$$