7.1.7 Check Your Understanding A right triangle has legs with lengths of 3s and 48. Select all true statements for the triangle. The hypotenuse of the triangle has a length of 58. The hypotenuse of the triangle has a length of 5 The hypotenuse of the triangle has a length of 25s. The area of the triangle is 12s^2 The area of the triangle is 6s^2 The area of the triangle is (s^2)/(6)

To determine the true statements about the right triangle with legs of lengths 3s and 48, we can use the Pythagorean theorem and the formula for the area of a triangle.<br /><br />1. The hypotenuse of the triangle has a length of 58.<br /> This statement is false. The hypotenuse of a right triangle is the longest side, and it is not equal to 58.<br /><br />2. The hypotenuse of the triangle has a length of 5.<br /> This statement is false. The hypotenuse of a right triangle is the longest side, and it is not equal to 5.<br /><br />3. The hypotenuse of the triangle has a length of 25s.<br /> This statement is true. According to the Pythagorean theorem, the square of the hypotenuse is equal to the sum of the squares of the other two sides. In this case, the hypotenuse is equal to the square root of (3s)^2 + 48^2, which simplifies to 25s.<br /><br />4. The area of the triangle is 12s^2.<br /> This statement is false. The area of a triangle is given by the formula 1/2 * base * height. In this case, the base is 3s and the height is 48, so the area is 1/2 * 3s * 48 = 72s.<br /><br />5. The area of the triangle is 6s^2.<br /> This statement is false. The area of a triangle is given by the formula 1/2 * base * height. In this case, the base is 3s and the height is 48, so the area is 1/2 * 3s * 48 = 72s.<br /><br />6. The area of the triangle is s^2/6.<br /> This statement is false. The area of a triangle is given by the formula 1/2 * base * height. In this case, the base is 3s and the height is 48, so the area is 1/2 * 3s * 48 = 72s.<br /><br />Therefore, the only true statement about the right triangle with legs of lengths 3s and 48 is that the hypotenuse of the triangle has a length of 25s.