Triangles & Pythagorean Triplets Practice Questions with Solutions

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Question 1
What is the hypotenuse of a right-angled triangle whose legs are 24 cm and 70 cm?
Question 2
An odd integer n = 13 is the shortest side of a primitive Pythagorean triplet (a, b, c). Find the hypotenuse c.
Question 3
An even integer n = 16 is the shortest side of a primitive Pythagorean triplet. What is the length of the hypotenuse?
Question 4
A right-angled triangle has legs of lengths 15 cm and 36 cm. What is its inradius?
Question 5
In a right triangle with legs 25 cm and 60 cm, find the length of the altitude drawn to the hypotenuse.
Question 6
The sides of a right-angled triangle are in the ratio 8:15:17. If its perimeter is 160 cm, what is its area?
Question 7
In a primitive Pythagorean triplet (a, b, c), the hypotenuse c and longer leg b differ by 1. If the shortest leg is 9, what is the value of b?
Question 8
A right-angled triangle has a hypotenuse of 29 cm and a perimeter of 70 cm. Find the length of its shortest leg.
Question 9
How many non-congruent right-angled triangles with integer sides have a hypotenuse of exactly 50 cm?
Question 10
An integer-sided right triangle has an area of 30 cm² and a perimeter of 30 cm. What is the length of its hypotenuse?