# Determine whether the given lengths can be sides of a right triangle. Which of the following are true statements. A.The lengths 7, 40 and 41 can not be sides of a right triangle. B.The lengths 12, 16, and 20 can not be sides of a right triangle. C.The lengths 7, 40 and 41 can not be sides of a right triangle.D.The lengths 12, 16, and 20 can be sides of a right triangle. The lengths 7, 40 and 41 can be sides of a right triangle.

• Subject:

Mathematics
• Author:

russo
• Created:

7 months ago

Given sides 12, 16 and 20 can be the sides of right triangle.

Step-by-step explanation:

Sides of right triangle always follow the Pythagoras theorem.

i.e (base)^2 + (Height)^2 = (Hypotenuse)^2

For the given Lengths 7, 40 and 41

We need to check if

7^2 + 40^2 =41^2 \\or\\ 7^2 + 40^2 \neq41^2

Since \\7^2 + 40^2 = 1649\\and \\41^2 = 1681

That means, \\ 7^2 + 40^2 \neq 41^2

hence 7,40 and 41 can not be the sides of right triangle.

Next,

Given sides 12,16 and 20.

Again follow the similar process used in the above problem.

12^2 + 16^2 =400\\And \\20^2 = 400\\Since 12^2 + 16^2 = 20^2

Therefore given sides 12,16 and 20 can be the sides of right triangle.

A. The lengths 7, 40 and 41 can not be sides of a right triangle. C. The lengths 7, 40 and 41 can not be sides of a right triangle. D. The lengths 12, 16, and 20 can be sides of a right triangle. Quick Answer: A and C are true statements. Explanation: In order for three lengths to form a right triangle, the lengths must satisfy the Pythagorean Theorem which states that the sum of the squares of two shorter sides must equal to the square of the longest side. For example, in a right triangle with sides 7, 40, and 41, 72 + 402 ≠ 412, so it does not satisfy the Pythagorean Theorem and therefore cannot be a right triangle. Similarly, 122 + 162 = 202, thus for the lengths 12, 16 and 20, they can form a right triangle.

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