Final answer:
The width of the rectangle is 4/5 in., and the height of the triangle does not match any of the provided options; the correct height should be 7/3 ft or 2 1/3 ft based on the given base and area.
Step-by-step explanation:
To find the width of a rectangle with given length and area, use the formula for area Area = length × width. Given the area of 12/15 in.² and the length of 1/3 in., we can set up an equation: 12/15 = (1/3) × width. Solving for width, we get width = (12/15) / (1/3). After simplifying, width = 4/5 in., which corresponds to option A.
To find the height of a triangle with a given base and area, use the formula Area = 1/2 × base × height. Given the area of 2 5/8 ft.² (which is 21/8 ft.² when converted to an improper fraction) and the base of 3/4 in., we can set up the equation: 21/8 = 1/2 × (3/4) × height. Solving for height, we find height = (2 × 21/8) / (3/4), which simplifies to height = 7/3 ft or 2 1/3 ft. However, none of the options given match this result, suggesting a possible error in the options provided.