Pythagorean Triples
45-45-90
30-60-90
Random
Miscellaneous
100

Do the following sides form a Pythagorean triple? √3, √4 and √5?

No

100

In a 45-45-90 triangle, if the hypotenuse is 12, what are the length of the legs?

6√2

100

If a side of an equilateral triangle is 6, what is the length of its altitude in simplest radical form?

3√3 

100

In an isosceles right triangle, if a leg is $, what is the length of $.

$√2.

100

If the legs of a right triangle are h and  4 + h, and they hypotenuse is 20, what is h?

12

200

In a right triangle, if the legs are 8 and 15, what is the perimeter of the triangle.

40.

200

If the side of a square is 6V3, find the length of its' diagonal.

6√6

200

In a 30-60-90 triangle the hypotenuse has a length of 4 feet. What is the perimeter of the triangle in simplest radical form?

6 + 2√3

200

If the distance between bases on a baseball diamond is 90 feet, how far is it from second base to home in simplest radical form?

90√2

200

If the altitude of an equilateral triangle is 18, what is the length of a side of the equilateral triangle?

12√3

300

If a lamppost 12 feet tall creates a shadow 5 feet long, what is the distance between the top of the lamppost and the part of the shadow farthest away from it?

13 feet

300

What is the area of a right triangle with a leg of 3 and a hypotenuse of 5?

6

300

What is the perimeter of a 30-60-90 triangle with a shortest leg having a length of 1 inch? Put your answer in simplest radical form.

3 +√3

300

Triangle PAB is a right triangle with right angle at B. Find the coordinates of P if P is in quadrant 1 for A(-3,1) and B(4,1).

(4,8)

300
In a 30-60-90 triangle, the longer leg has a value of 24. What is the length of the hypotenuse in simplest radical form?
16√3
400

In a right triangle, if a leg is 7 and the hypotenuse if 25, what is the length of the other leg.

24.

400

The length of a leg of an isosceles right triangle is 20√5 cm. What is the length of the hypotenuse? Leave your answer in simplest radical form.

20√10

400

If the long leg of a 30-60-90 triangle is 9, what is the hypotenuse?

6√3.

400
If a tree is 2 feet tall and makes a 90 degree angle with the ground, how far away is a 4 foot ladder from the tree if the ladder makes a 30 degree angle with the ground and a 60 degree angle with the tree? Leave your answer in simplest radical form.
2√3 feet
400
If a roof makes a 30-60-90 triangle with a hypotenuse of 10 and a shorter leg of 5, what is the length of the longer leg? Leave your answer in simplest radical form.
5√3
500

In a rectangle with side lengths of 9 and 40, what is the diagonal?

41

500

In a square with a diagonal of 3√2, what is the perimeter of the square?

12 units

500

If the shortest leg of a 30-60-90 triangle is 5√6, what is the length of the long leg in simplest radical form?

15√2

500

Given right triangle with legs of a, and a +1 and hypotenuse of a + 2, find a.

3

500
If one diagonal of a square has a length of 4√2, what is the perimeter of the square?
16
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