If the lengths of both legs of a right triangle are 2, then what is the length of its hypotenuse?
2.83
4
1.33
0.14
If the two sides of a right triangle are 2.8 cm and 4.5 cm, then find the length of the hypotenuse.
4.3 cm
5.3 cm
6.3 cm
7.3 cm
The length of the hypotenuse can be found using the Pythagorean theorem, which states that the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides.
Using this theorem, the length of the hypotenuse can be calculated as follows:
Hypotenuse^2 = Leg1^2 + Leg2^2
Hypotenuse^2 = 2^2 + 2^2
Hypotenuse^2 = 4 + 4
Hypotenuse^2 = 8
Taking the square root of both sides gives us:
Hypotenuse = √8
The value of √8 is approximately 2.83.
Therefore, the length of the hypotenuse is 2.83.
Megan has a piece of fabric which is a right triangular shape. The length of leg 1 is 4 m. The length of the other leg is twice the length of leg 1. What would be the length of the third side of the fabric?
8.94 m
7.21 m
6.93 m
4.47 m
To find the length of the third side (hypotenuse) of the right triangle, we can use the Pythagorean theorem.
The Pythagorean theorem states that the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides.
In this case, if leg 1 is 4 m, then the length of the other leg would be twice that, which is 4 x 2 = 8 m.
Now, let's find the length of the hypotenuse.
Hypotenuse^2 = Leg1^2 + Leg2^2
Hypotenuse^2 = 4^2 + 8^2
Hypotenuse^2 = 16 + 64
Hypotenuse^2 = 80
Now, taking the square root of both sides gives us:
Hypotenuse = √80
The value of √80 is approximately 8.94 m.
Therefore, the length of the third side (hypotenuse) of the fabric is 8.94 m.
Which of the following is a Pythagorean triplet?
(5, 9, 13)
(5, 12, 13)
(17, 12, 13)
(5, 12, 15)
A Pythagorean triplet is a set of three positive integers (a, b, c) that satisfy the equation a^2 + b^2 = c^2, where c is the length of the hypotenuse of a right triangle.
Let's check each option:
1. (5, 9, 13):
5^2 + 9^2 = 25 + 81 = 106.
13^2 = 169.
Therefore, (5, 9, 13) is not a Pythagorean triplet.
2. (5, 12, 13):
5^2 + 12^2 = 25 + 144 = 169.
13^2 = 169.
So, (5, 12, 13) is a Pythagorean triplet.
3. (17, 12, 13):
17^2 + 12^2 = 289 + 144 = 433.
13^2 = 169.
Therefore, (17, 12, 13) is not a Pythagorean triplet.
4. (5, 12, 15):
5^2 + 12^2 = 25 + 144 = 169.
15^2 = 225.
So, (5, 12, 15) is not a Pythagorean triplet.
Therefore, the Pythagorean triplet among the given options is (5, 12, 13).
Sam buys a carpet for his apartment. The diagonal length of the carpet is 12 feet and the width is 10 feet. Find the length of the carpet.
8 feet
6.633 feet
3 feet
4.5 feet
To find the length of the carpet, we can use the Pythagorean theorem.
The Pythagorean theorem states that the square of the length of the hypotenuse (diagonal in this case) is equal to the sum of the squares of the lengths of the other two sides.
In this case, the width is given as 10 feet, and the diagonal length is given as 12 feet.
Let's denote the length of the carpet as L.
Using the Pythagorean theorem, we can set up the following equation:
L^2 + 10^2 = 12^2
Simplifying the equation gives us:
L^2 + 100 = 144
Subtracting 100 from both sides:
L^2 = 144 - 100
L^2 = 44
Now, taking the square root of both sides:
L = √44
The value of √44 is approximately 6.633 feet.
Therefore, the length of the carpet is approximately 6.633 feet.
To find the length of the hypotenuse of a right triangle, we can use the Pythagorean theorem.
The Pythagorean theorem states that the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides.
In this case, the two sides are given as 2.8 cm and 4.5 cm.
Let's denote the length of the hypotenuse as H.
Using the Pythagorean theorem, we can set up the following equation:
H^2 = (2.8 cm)^2 + (4.5 cm)^2
Simplifying the equation gives us:
H^2 = 7.84 cm^2 + 20.25 cm^2
H^2 = 28.09 cm^2
Now, taking the square root of both sides:
H = √28.09 cm
The value of √28.09 cm is approximately 5.3 cm.
Therefore, the length of the hypotenuse is approximately 5.3 cm.
Find the statement which does not represent the Pythagorean Theorem if a and b are the legs and c is the hypotenuse.
a2 + b2 = c2
a2 - b2 = c2
a2 = c2 -b2
b2 = c2 - a2