4. The legs of a right triangle measure 24 feet and 45 feet. What is the length of the hypotenuse? (1 point)
51 ft
69 ft
38.07 ft
8.31 ft
5. Which of these cannot represent the lengths of the sides of a right triangle? (1 point)
3 ft, 4 ft, 5 ft
6 in., 8 in., 10 in.
16 cm, 63 cm, 65 cm
8 m, 9 m, 10 m
To solve these questions, we can use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the two legs.
4. The legs of the right triangle measure 24 feet and 45 feet. To find the length of the hypotenuse, we can use the Pythagorean theorem:
Applying the theorem, we have:
(Length of Hypotenuse)^2 = (Length of Leg 1)^2 + (Length of Leg 2)^2
(Length of Hypotenuse)^2 = 24^2 + 45^2
(Length of Hypotenuse)^2 = 576 + 2025
(Length of Hypotenuse)^2 = 2601
To get the length of the hypotenuse, we take the square root of both sides:
Length of Hypotenuse = √2601 = 51 ft
Therefore, the length of the hypotenuse is 51 ft.
5. To determine which set of values cannot represent the lengths of the sides of a right triangle, we can again use the Pythagorean theorem.
Let's check each set of values:
a) 3 ft, 4 ft, 5 ft:
(Length of Hypotenuse)^2 = (Length of Leg 1)^2 + (Length of Leg 2)^2
Hence, 5^2 = 3^2 + 4^2 becomes 25 = 9 + 16, which is true. Therefore, this set of values can represent the lengths of the sides of a right triangle.
b) 6 in., 8 in., 10 in.:
Similar to the above calculation, we find that 10^2 = 6^2 + 8^2 becomes 100 = 36 + 64, which is true. Therefore, this set of values can represent the lengths of the sides of a right triangle.
c) 16 cm, 63 cm, 65 cm:
Similarly, 65^2 = 16^2 + 63^2 becomes 4225 = 256 + 3969, which is true. Therefore, this set of values can represent the lengths of the sides of a right triangle.
d) 8 m, 9 m, 10 m:
Finally, we have 10^2 = 8^2 + 9^2, which becomes 100 ≠ 64 + 81. Here, the equation is false.
Therefore, the set of values that cannot represent the lengths of the sides of a right triangle is 8 m, 9 m, 10 m.
these depend on the Pythagorean Theorem:
a^2+b^2+c^2
for #4, just plug in your numbers
for #5, test each set till one fits the theorem.