Final answer:
To find the altitude to the 15-inch side of a right-angled triangle (9, 12, 15 inches), calculate the area using the other two sides, and then use that area to solve for the altitude, which ends up being 7.2 inches.
Step-by-step explanation:
To find the length of the altitude to the 15-inch side of a triangle with side lengths 9, 12, and 15 inches, we can use the Pythagorean theorem or recognize that the triangle is a right-angled triangle with a hypotenuse of 15 inches (since 9, 12, and 15 forms a Pythagorean triple). Thus, the altitude to the hypotenuse (which is the same as the altitude to the 15-inch side) can be found by applying the formula for the area of a triangle, which is (base × height) / 2.
The area can also be calculated using the lengths of the two other sides (9 and 12 inches) as base and height since they are perpendicular. So,
Area = (9 inches × 12 inches) / 2 = 54 square inches.
We can then set up the equation for the area using the 15-inch side as the base and the unknown altitude (h) as the height:
54 square inches = (15 inches × h) / 2
Multiplying both sides of the equation by 2 and dividing by 15 gives us:
h = (2 × 54) / 15 = 108 / 15 = 7.2 inches.
The altitude to the 15-inch side of the triangle is therefore 7.2 inches.