Question

The given lengths are two sides of a right triangle. All three side lengths of the triangle are integers, and together they form a Pythagorean triple. Find the length of the third side, then indicate whether it is a leg or a hypotenuse.

28, 96

A. 37, leg
B. 54, leg
C. 92, leg
D. 100, hypotenuse

Answer 1

28, 96 100, hypotenuse
Pythagorean theorem
h2=l2+l2
100^2=28^2+96^2
10000=10000

Answer 2

The correct answer is: Option (D) 100, hypotenuse

Step-by-step explanation:

Pythagorean theorem is written in mathematical form as follows:

(hypotenuse)^2 = (perpendicular)^2 + (base)^2

perpendicular and base are called the legs of a right-angled triangle.

Let's suppose that 28 and 96 are the legs of triangle, then by applying the Pythagorean theorem, we would get the hypotenuse as follows:

(hypotenuse)^2 = (28)^2 + (96)^2

(hypotenuse)^2 = 10,000

Take square-root on both sides:

hypotenuse = 100 (Option D)

Let's suppose 96 is a hypotenuse, and 28 is one leg (let's say base) of a right-angled triangle, then:

(96)^2 = (28)^2 + (leg)^2

leg =
`√(96^2 - 38^2) = 4√(527)` (not an option)

Hence the correct answer is Option (D) 100, hypotenuse.