1. **State the problem:** We have a rectangle CDGH with sides labeled as follows: - Top side DG = $x + 10$ - Right side GH = $x + 7$ - Bottom side CH = $3y - 3$ - Left side DC = $2y$ We need to find the values of $x$ and $y$. 2. **Recall properties of rectangles:** Opposite sides of a rectangle are equal in length. 3. **Set up equations:** - Since DG and CH are opposite sides, they are equal: $$x + 10 = 3y - 3$$ - Since GH and DC are opposite sides, they are equal: $$x + 7 = 2y$$ 4. **Solve the system of equations:** From the second equation: $$x + 7 = 2y \implies x = 2y - 7$$ Substitute $x = 2y - 7$ into the first equation: $$2y - 7 + 10 = 3y - 3$$ Simplify: $$2y + 3 = 3y - 3$$ 5. **Isolate $y$:** $$2y + 3 = 3y - 3$$ $$3 + 3 = 3y - 2y$$ $$6 = y$$ 6. **Find $x$ using $y=6$:** $$x = 2(6) - 7 = 12 - 7 = 5$$ 7. **Final answer:** $$x = 5, \quad y = 6$$