Two opposite sides of a rectangle are (5x + 3) m and (2x + 9) m. If an adjacent side is (6x - 7) m, find in m$^2$, the area of the rectangle.

Analyze the question

Opposite sides of a rectangle are equal, so (5x + 3) = (2x + 9). This gives x, and then we can find the adjacent side and the area.

Solve for x

5x + 3 = 2x + 9 3x = 6 x = 2

Find the sides

• Length: 5(2) + 3 = 13 m (check: 2(2) + 9 = 13 m ✓)
• Adjacent side (width): 6(2) − 7 = 12 − 7 = 5 m

Area

Area = 13 × 5 = 65 m²

Answer: The area is 65 m², which is option B.

Tip: In any rectangle question that gives algebraic expressions for opposite sides, always set them equal first. This is the key step that unlocks x. Then substitute into the remaining side and multiply.