Page 149: Figure It Out

Question 1: Combined Rectangles

Problem: Find dimensions of a rectangle with area equal to sum of ($5 \times 10$) and ($2 \times 7$).

• Area 1 = 50.
• Area 2 = 14.
• Total Area = 64.
• Possible Dimensions:
  • $8 \times 8$ (Square)
  • $16 \times 4$
  • $32 \times 2$
  • $64 \times 1$

Question 2: Garden Width

Problem: Length 50 m, Area 1000 sq m.

• Width = $1000 / 50 = 20\text{ m}$.

Question 3: Carpet Area

Problem: Floor ($5 \times 4$), Carpet ($3 \times 3$). Uncarpeted area?

• (Same as Solved Example).
• $20 - 9 = 11\text{ sq m}$.

Question 4: Flower Beds

Problem: Garden $15 \times 12$. Four beds ($2 \times 1$) at corners. Area of lawn?

1. Total Garden Area: $15 \times 12 = 180\text{ sq m}$.
2. Area of 1 Flower Bed: $2 \times 1 = 2\text{ sq m}$.
3. Total Flower Bed Area: $4 \times 2 = 8\text{ sq m}$.
4. Lawn Area: $180 - 8 = 172\text{ sq m}$.

Question 8: Folded Square

Problem: A square is folded in half and cut into two rectangles. Which statement is true?

• c. The perimeters of both rectangles added together is always $1\frac{1}{2}$ times the perimeter of the square.

Proof:

• Square side = $s$. Perimeter $P_{sq} = 4s$.
• Rectangle sides = $s$ and $s/2$.
• Perimeter of 1 Rectangle = $2(s + s/2) = 2(1.5s) = 3s$.
• Sum of 2 Rectangles = $3s + 3s = 6s$.
• Ratio: $6s / 4s = 1.5$ ($1\frac{1}{2}$).
• Statement C is True.