Question: Topic: solve real-life problems involving scales in maps, blueprints, and sketches
1. A scale drawing has been drawn below of a shed that a garden planner wants to build. The scale used for the drawing is 1:25. The area that the shed will be built on is a rectangle which measures 5.1 m by 4 m. Will the shed fit into the space allocated?
15.2 cm
12.5 cm
Consider this as your guide:
a. Identify the scale being used.
b. Convert the dimensions of the drawing to actual dimensions.
c. Convert the units if necessary.
d. Compare with the available space
position_hint: top-left
L-shape figure: the shaded blueprint is an L-shaped rectangle-like polygon, with the vertical leg on the left and the horizontal leg along the bottom; position_hint: bottom-left
1. **State the problem:** We have a scale drawing of a shed with dimensions $15.2\text{ cm}$ by $12.5\text{ cm}$ drawn at a scale of $1:25$. The actual space available for the shed is a rectangle measuring $5.1\text{ m}$ by $4\text{ m}$. We need to determine if the shed will fit in the allocated space.
2. **Identify the scale:** The scale $1:25$ means that $1\text{ cm}$ on the drawing represents $25\text{ cm}$ in real life.
3. **Convert the drawing dimensions to actual dimensions:**
$$\text{Actual length} = 15.2\text{ cm} \times 25 = 380\text{ cm}$$
$$\text{Actual width} = 12.5\text{ cm} \times 25 = 312.5\text{ cm}$$
4. **Convert actual dimensions to meters:**
$$380\text{ cm} = \frac{380}{100} = 3.8\text{ m}$$
$$312.5\text{ cm} = \frac{312.5}{100} = 3.125\text{ m}$$
5. **Compare with the available space:**
- Available length: $5.1\text{ m}$
- Available width: $4\text{ m}$
Since $3.8\text{ m} \leq 5.1\text{ m}$ and $3.125\text{ m} \leq 4\text{ m}$, the shed will fit into the space allocated.
**Final answer:** Yes, the shed will fit into the space allocated.