David’s study table is 20 inches long. If the diagonal measures 25 inches, find the width of David’s study table.
15 inches
20 inches
25 inches
45 inches
To find the width of David's study table, we can use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (diagonal) is equal to the sum of the squares of the lengths of the other two sides.
Let the width of the study table be x inches. Using the Pythagorean theorem, we have:
x^2 + 20^2 = 25^2
x^2 + 400 = 625
x^2 = 225
x = 15
Therefore, the width of David's study table is 15 inches.
The floor is in the shape of square. Louis measures the area as 445 square feet. Find the diagonal of the floor.
21.09 ft
22 ft
29.83 ft
30. 50 ft
To find the diagonal of the square floor, we can use the Pythagorean theorem.
Let s be the length of one side of the square floor. The area of a square is given by A = s^2.
We are given that the area of the floor is 445 square feet. We can set up the equation:
s^2 = 445
Taking the square root of both sides, we find:
s = √445 ≈ 21.09
Since the diagonal of a square forms a right triangle with each side of the square, we can use the Pythagorean theorem to find the diagonal, d:
d^2 = s^2 + s^2
d^2 = 2s^2
d = √(2s^2) = √(2 * 21.09^2) ≈ 29.83
Therefore, the diagonal of the floor is approximately 29.83 feet.
An ice cream cone is created for the New Year’s Eve. The height of the cone from the ground level is 15 feet and the diameter of the cone is one foot more than the height. Which of the following measures the slant height of the cone?
17 feet
17.89 feet
20.52 feet
21.93 feet
The slant height of the cone can be found using the Pythagorean theorem. The slant height, height, and radius of the cone form a right triangle.
Let the height of the cone be h, and the diameter be d. We are given that h = 15 feet and d = h + 1 feet.
The radius of the cone, which is half the diameter, can be found by dividing d by 2:
r = (h + 1) / 2
The slant height, s, can be found using the Pythagorean theorem:
s^2 = r^2 + h^2
Substituting the values we have:
s^2 = ((h + 1) / 2)^2 + h^2
s^2 = (h^2 + 2h + 1) / 4 + h^2
s^2 = (2h^2 + 2h + 1) / 4
Multiplying both sides by 4:
4s^2 = 2h^2 + 2h + 1
4s^2 = 2(h^2 + h) + 1
Since h = 15:
4s^2 = 2(15^2 + 15) + 1
4s^2 = 2(225 + 15) + 1
4s^2 = 2(240) + 1
4s^2 = 480 + 1
4s^2 = 481
Taking the square root of both sides:
s = √481 ≈ 21.93 feet
Therefore, the slant height of the cone is approximately 21.93 feet.
Find the height of the wall.
10.2 m
10.4 m
10.6 m
10.8 m