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Charra [1.4K]
2 years ago
5

The lengths of two sides of a triangle are 10 and 24, and the third side is x. How many whole number values are possible for x.

Mathematics
1 answer:
solong [7]2 years ago
5 0

Answer:

20.

Step-by-step explanation:

In any triangle, the sum of the lengths of any two sides should be strictly greater than the length of the third side. For example, if the length of the three sides are a, b, and c:

a + b > c,

a + c > b, and

b + c > a.

In this question, the length of the sides are 10, 24, and x. The length of these sides should satisfty the following inequalities:

10 + 24 > x,

10 + x > 24, and

24 + x > 10.

Since x > 0, the inequality 24 + x > 10 is guarenteed to be satisfied.

Simplify 10 + 24 > x to obtain the inequality x < 35.

Similarly, simplify 10 + x > 24 to obtain the inequality x > 14.

Since x needs to be a whole number, the greatest x that satisfies x < 35 would be 34. Similarly, the least x\! that satisfies x > 14 would be 15. Thus, x\!\! could be any whole number between 15\! and 34\! (inclusive.)

There are a total of 34 - 15 + 1 = 20 distinct whole numbers between 15 and 34 (inclusive.) Thus, the number of possible whole number values for x would be 20.

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