An acute triangle has two sides measuring 8 cm and 10 cm. What is the best representation of the possible range of values for the third side, s?

Question

04-10-2016
Mathematics

contestada

An acute triangle has two sides measuring 8 cm and 10 cm. What is the best representation of the possible range of values for the third side, s?

Respuesta :

Otras preguntas

What mountain range forms the Italian Peninsula's northern border? the Italian Alps the Adriatic Mountains the Apennines the Tyrrhenian Alps

The equation below has one solution. 9 x minus 10 = 3 x + 2 What is the solution to the equation? –2 –1 1 2

Avery uses a blend of dark chocolate and milk chocolate to make the ice cream topping at her restaurant. She wants to buy 10 kg more of dark chocolate than milk

24 and 32 are the given lengths of a right triangle with the unknown length (x) being 40, how do I tell if its a leg or the hypotenuse?

A bag contains cards numbered 1-20. Find the probability. Round your answer to 2 decimal places. Selecting 2 odd numbers when 2 slips are chosen without replace

In the context of independence versus connectedness, which of the following is true of women's vocations in general? Women more than men value earnings, promoti

Which BEST describes the author's technique in this sentence? Joining the battle, the belligerent boy beat his chest to show his resolve. A) The author creates

how would i find the answer to 3^2

Jessie purchased a used car from a small business. They offered to let him finance or borrow $3200 for a term of 2 years at 11% a year using simple interest. Ho

During Mendel's first set of experiments, he allowed true-breeding tall plants to cross with true-breeding short plants. What happened when he allowed the Fy o

olemakpadu olemakpadu · Answer 1 · 2016-10-04T21:34:49+02:00

The third side of any triangle must be greater than the difference of the given two sides and must be less than the sum of the given two sides.

Given 8cm and 10cm.

The third side s,

s > (10 - 8) s < (10 + 8)
s > 2 s < 18

s > 2 and s < 18 .

Combining the two inequalities:

2 < s < 18 Range is between 2 and 18.

So the range for third side is a number between 2 and 18 cm. Note that 2 and 18 are not included.

s could be any of 3, 4, 5, 7, 9, 13,..17. I hope this helps.

calculista calculista · Answer 2 · 2018-12-01T14:53:47+01:00

Answer:

The solution for s is the interval--------> [tex](2,18)[/tex]

All real numbers greater than [tex]2[/tex] and less than [tex]18[/tex]

Step-by-step explanation:

we know that

The Triangle Inequality Theorem, states that the sum of the lengths of any two sides of a triangle is greater than the length of the third side

so

Let

s-----> the third length side of the given triangle

Applying the triangle inequality theorem

[tex]8+10> s[/tex]

[tex]18> s[/tex] -------> [tex]s<18\ cm[/tex]

[tex]8+s> 10[/tex]

[tex]s> 10-8[/tex]

[tex]s> 2\ cm[/tex]

The solution for s is the interval--------> [tex](2,18)[/tex]

All real numbers greater than [tex]2[/tex] and less than [tex]18[/tex]