Mathematics, 25.08.2019 13:30 gokusupersaiyan12345

The shorter sides of an acute triangle are x cm and 2x cm. the longest side of the triangle is 15 cm. what is the smallest possible whole-number value of x? 6 7 8 9

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The longest side in the triangle is opposite to the largest angle of this triangle. If triangle is acute, then all angles are acute. Acute angle has cosine that is positive.

Use cosine theorem to determine the cosine of the largest angle:

$15^2=x^2+(2x)^2-2\cdot x\cdot 2x\cdot \cos \alpha,$ where $\alpha$ is the largest angle.

Then

$225=x^2+4x^2-4x^2\cos \alpha,\\ \\\cos \alpha=\dfrac{225-5x^2}{-4x^2}=\dfrac{5x^2-225}{4x^2}.$

Since $\cos \alpha0,$ then

$\dfrac{5x^2-225}{4x^2}0\Rightarrow 5x^2-2250.$

Divide this inequality by 5:

$x^2-450,\\ \\(x-3\sqrt{5})(x+3\sqrt{5})0,\\ \\x\in (-\infty,-3\sqrt{5})\cup (3\sqrt{5},\infty).$

Note that $3\sqrt{5}\approx 6.71,$ then the smallest possible whole-number value of x is 7.

correct choice is B

Answer from: sierralynnbaldp16d4b

The value of x is 7

B is correct

Step-by-step explanation:

Three sides of triangle are x cm, 2x cm and 15 cm.

In a triangle

Sum of two smallest side is greater than third side.Difference of two smallest side is less than third side.

Sum of two side is greater than 3rd side

x + 2x > 15

3x > 15

x > 5

Thus, x must be greater than 5

Difference of two sides is less than 3rd side

2x - x < 15

x < 15

Thus, x must be less than 15

Using cosine rule,

$\cos A=\dfrac{b^2+c^2-a^2}{2bc}$

Triangle is acute, Cos A>0

where, a=x , b=2x and c=15

$\dfrac{x^2+(2x)^2-15^2}{2\cdot x\cdot 2x}0$

5x^2-2250

$x 3\sqrt5\approx 6.7$

$x< -3\sqrt5\approx -6.7$

x and 2x is shorter sides.

2x<15 or x<7.5

Possible value of x>6.7 and x<7.5

Hence, The value of x is 7

Answer from: Quest

Were is the problem

Answer from: Quest

step-by-step explanation:

the 2000 florida legislature amended section 322.05, florida statutes, changing the requirements to obtain a class e license for a driver under the age of 18 holding a learner's license. the following requirements must be met in order to obtain a regular class e license if a learner's license is issued on or after october 1, 2000:

must hold a learner's license for at least 12 months or until the 18th birthday.

must have no convictions 12 months from the issue date of the learner's license.

may have one traffic conviction within 12 months from the issue date of the learner's license if adjudication is withheld.

a parent, legal guardian, or responsible adult over 21 years old must certify that the driver has 50 hours driving experience, including 10 hours of night time driving.

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The shorter sides of an acute triangle are x cm and 2x cm. the longest side of the triangle is 15 cm...

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