Determine the length of the missing side in the triangle shown.
right triangle with one leg labeled 12 and hypotenuse labeled 14
a) square root of 2
b) square root of 26
c) square root of 52
d) square root of 340
In a right triangle, according to the Pythagorean theorem, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides.
Let's denote the missing side as x.
Given that one leg is labeled 12 and the hypotenuse is labeled 14, we can set up the equation as follows:
12^2 + x^2 = 14^2
Simplifying:
144 + x^2 = 196
Subtracting 144 from both sides:
x^2 = 52
Taking the square root of both sides:
x = √52
Simplifying further:
x = √(4 * 13)
x = √(2^2 * 13)
x = 2√13
Therefore, the length of the missing side is 2√13.
The correct answer is not listed among the given options.
Determine which set of side measurements could be used to form a triangle.
a) 15, 6, 21
b) 14, 18, 5
c) 7, 4, 2
d) 6, 24, 14
To determine if a set of side measurements can form a triangle, we need to check if the sum of the lengths of the two shorter sides is greater than the length of the longest side.
Let's go through each option:
a) 15, 6, 21
15 + 6 = 21
21 > 21
This set of side measurements can form a triangle.
b) 14, 18, 5
14 + 5 = 19
19 > 18
This set of side measurements can form a triangle.
c) 7, 4, 2
2 + 4 = 6
6 < 7
This set of side measurements cannot form a triangle.
d) 6, 24, 14
6 + 14 = 20
20 > 24
This set of side measurements can form a triangle.
Therefore, the sets of side measurements that can form a triangle are options a) 15, 6, 21, b) 14, 18, 5, and d) 6, 24, 14.
Can a triangle be formed with side lengths 13, 7, and 5? Explain.
a) Yes, because 13 + 7 > 5
b) Yes, because 13 + 5 < 7
c) No, because 5 + 7 < 13
d) No, because 5 + 7 > 13
In order for a triangle to be formed, the sum of the lengths of the two shorter sides must be greater than the length of the longest side.
Let's check the given side lengths:
5 + 7 = 12
12 < 13
Since the sum of the lengths of the two shorter sides (5 and 7) is less than the length of the longest side (13), a triangle cannot be formed.
Therefore, the correct answer is:
c) No, because 5 + 7 < 13
The shortest side of a right triangle measures 5, and the longest side measures 13. Determine the measurement of the unknown side.
a) 4
b) 11
c) 13
d) 12
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 other two sides, according to the Pythagorean theorem.
Let's denote the unknown side as x.
Given that the shortest side measures 5 and the longest side measures 13, we can set up the equation as follows:
5^2 + x^2 = 13^2
25 + x^2 = 169
Subtracting 25 from both sides:
x^2 = 144
Taking the square root of both sides:
x = √144
Simplifying further:
x = 12
Therefore, the measurement of the unknown side is 12.
The correct answer is:
d) 12
Determine which set of side measurements could be used to form a right triangle.
a) 4, 8, 11
b) 6, 8, 13
c) square root of 3, square root of 5, 8
d) square root of 3, square root of 13, 4
To determine if a set of side measurements can form a right triangle, we can use the Pythagorean theorem. The Pythagorean theorem 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 other two sides.
Let's check each option:
a) 4, 8, 11
Using the Pythagorean theorem:
4^2 + 8^2 = 16 + 64 = 80
11^2 = 121
80 ≠ 121
This set of side measurements cannot form a right triangle.
b) 6, 8, 13
Using the Pythagorean theorem:
6^2 + 8^2 = 36 + 64 = 100
13^2 = 169
100 ≠ 169
This set of side measurements cannot form a right triangle.
c) √3, √5, 8
Using the Pythagorean theorem:
(√3)^2 + (√5)^2 = 3 + 5 = 8
8^2 = 64
8 = 8
This set of side measurements can form a right triangle.
d) √3, √13, 4
Using the Pythagorean theorem:
(√3)^2 + (√13)^2 = 3 + 13 = 16
4^2 = 16
16 = 16
This set of side measurements can also form a right triangle.
Therefore, the sets of side measurements that can form a right triangle are options c) √3, √5, 8, and d) √3, √13, 4.
A rectangular pool is 6 meters wide and 14 meters long. If you swim diagonally from one corner to the other, how many meters will you swim? Approximate the answer to the nearest tenth.
a) 2.8 meters
b) 15.2 meters
c) 4.3 meters
d) 12.6 meters