Question: 1. These triangles are similar. Find the area of the smaller triangle to the nearest whole number. 105 ft² 16 ft 12 ft top-left: Large triangle with area 105 ft² and base 16 ft. bottom-right: Smaller similar triangle with base 12 ft.

1. **State the problem:** We have two similar triangles. The larger triangle has an area of $105$ ft$^2$ and a base of $16$ ft. The smaller triangle has a base of $12$ ft. We need to find the area of the smaller triangle. 2. **Recall the formula for areas of similar triangles:** The ratio of the areas of two similar triangles is equal to the square of the ratio of their corresponding sides. $$\frac{\text{Area}_{small}}{\text{Area}_{large}} = \left(\frac{\text{side}_{small}}{\text{side}_{large}}\right)^2$$ 3. **Set up the ratio using the given bases:** $$\frac{\text{Area}_{small}}{105} = \left(\frac{12}{16}\right)^2$$ 4. **Calculate the ratio of the sides squared:** $$\left(\frac{12}{16}\right)^2 = \left(\frac{3}{4}\right)^2 = \frac{9}{16}$$ 5. **Find the area of the smaller triangle:** $$\text{Area}_{small} = 105 \times \frac{9}{16}$$ 6. **Simplify the multiplication:** $$105 \times \frac{9}{16} = \frac{105 \times 9}{16} = \frac{945}{16}$$ 7. **Divide to get the decimal value:** $$\frac{945}{16} = 59.0625$$ 8. **Round to the nearest whole number:** $$59.0625 \approx 59$$ **Final answer:** The area of the smaller triangle is approximately **59** ft$^2$.