Right Triangles
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Math › Right Triangles
In order to get to work, Jeff leaves home and drives 4 miles due north, then 3 miles due east, followed by 6 miles due north and, finally, 7 miles due east. What is the straight line distance from Jeff’s work to his home?
2√5
11
10√2
15
6√2
Explanation
Jeff drives a total of 10 miles north and 10 miles east. Using the Pythagorean theorem (a2+b2=c2), the direct route from Jeff’s home to his work can be calculated. 102+102=c2. 200=c2. √200=c. √100√2=c. 10√2=c
What is the hypotenuse of a right triangle with side lengths 
Explanation
The Pythagorean Theorem states that 
Take 
Now we can start solving for 
The length of the hypotenuse is 
If 
Explanation
The formula for area of a triangble is 
Since 
Plug in our given values to solve:
In order to get to work, Jeff leaves home and drives 4 miles due north, then 3 miles due east, followed by 6 miles due north and, finally, 7 miles due east. What is the straight line distance from Jeff’s work to his home?
2√5
11
10√2
15
6√2
Explanation
Jeff drives a total of 10 miles north and 10 miles east. Using the Pythagorean theorem (a2+b2=c2), the direct route from Jeff’s home to his work can be calculated. 102+102=c2. 200=c2. √200=c. √100√2=c. 10√2=c
A right triangle has legs of 15m and 20m. What is the length of the hypotenuse?
30m
45m
35m
40m
25m
Explanation
The Pythagorean theorem is a2 + b2 = c2, where a and b are legs of the right triangle, and c is the hypotenuse.
(15)2 + (20)2 = c2 so c2 = 625. Take the square root to get c = 25m
What is the hypotenuse of a right triangle with side lengths
Explanation
The Pythagorean Theorem states that
Take
Now we can start solving for
The length of the hypotenuse is
If
Explanation
The formula for area of a triangble is
Since
Plug in our given values to solve:
In the figure above, 
Explanation
Assigning the length of ED the value of x, the value of AE will be 3_x_. That makes the entire side AD equal to 4_x_. Since the figure is a square, all four sides will be equal to 4_x_. Also, since the figure is a square, then angle A of triangle ABE is a right angle. That gives triangle ABE sides of 3_x_, 4_x_ and 10. Using the Pythagorean theorem:
(3_x_)2 + (4_x_)2 = 102
9_x_2 + 16_x_2 = 100
25_x_2 = 100
_x_2 = 4
x = 2
With x = 2, each side of the square is 4_x_, or 8. The area of a square is length times width. In this case, that's 8 * 8, which is 64.
A right triangle has legs of 15m and 20m. What is the length of the hypotenuse?
30m
45m
35m
40m
25m
Explanation
The Pythagorean theorem is a2 + b2 = c2, where a and b are legs of the right triangle, and c is the hypotenuse.
(15)2 + (20)2 = c2 so c2 = 625. Take the square root to get c = 25m
In the figure above,
Explanation
Assigning the length of ED the value of x, the value of AE will be 3_x_. That makes the entire side AD equal to 4_x_. Since the figure is a square, all four sides will be equal to 4_x_. Also, since the figure is a square, then angle A of triangle ABE is a right angle. That gives triangle ABE sides of 3_x_, 4_x_ and 10. Using the Pythagorean theorem:
(3_x_)2 + (4_x_)2 = 102
9_x_2 + 16_x_2 = 100
25_x_2 = 100
_x_2 = 4
x = 2
With x = 2, each side of the square is 4_x_, or 8. The area of a square is length times width. In this case, that's 8 * 8, which is 64.