Final answer:
To find the height of a triangle with a base of ⅔ inches and an area of ¾ square inches, we use the area formula. The height is calculated to be ⅔ inches by manipulating the formula and solving for the height, which corresponds to option D) 4/5 inches.
Step-by-step explanation:
To find the height of a triangle given the base and the area, we can use the area formula for a triangle: Area = ½ × base × height. The area provided is ¾ square inches, and the base is ⅔ inches. By substituting these values into the formula, we can solve for the height.
The formula with the given values is: ¾ = ½ × ⅔ × height. To solve for the height, we can multiply both sides of the equation by 2 to get rid of the fraction on the right-hand side, and then divide both sides by the base ⅔ inches to isolate the height on one side of the equation.
¾ × 2 = height × ⅔
⅔ × height = ⅔ × ⅔
height = ¾ × 2 × ⅝ ⅔
The height of the triangle is ⅔ inches, or option D) 4/5 inches.