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2 years ago

Suppose a triangle has sides a, b, and c and the angle opposite the side of length a is acute what must be true?

Mathematics

1 answer:

ANTONII [103]2 years ago

4 0

The true statement about the triangle is (a) b^2 + c^2 > a^2

<h3>How to determine the true inequality?</h3>

The sides are given as:

a, b and c

The angle opposite of side length a is an acute angle

The above means that:

The side a is the longest side of the triangle.

The Pythagoras theorem states that:

a^2 = b^2 + c^2

Since the triangle is not a right triangle, and the angle opposite a is acute.

Then it means that the square of a is less than the sum of squares of other sides.

This gives

a^2 < b^2 + c^2

Rewrite as:

b^2 + c^2 > a^2

Hence, the true statement about the triangle is (a) b^2 + c^2 > a^2

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2 1/2 divided by 2 2/3

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The height of a triangle is 4 sqrt 3 . What is the perimeter of the equatorial triangle?

Karo-lina-s [1.5K]

The perimeter of the equatorial triangle is 24 units

<h3><u>Solution:</u></h3>

Given that,

An equilateral triangle has an height equal to $4 \sqrt{3}$

The triangle is shown below

From Triangle ABC in the shown figure AD $=4 \sqrt{3}$

Let the sides of the equilateral triangle be ‘a’

AB = BC = a

Since, it is an equilateral triangle we get,

BD = DC = a ÷ 2

Now, using Pythagoras Theorem in Triangle ABD,

The Pythagorean theorem is this: In a right triangle, the sum of the squares of the lengths of the two legs is equal to the square of the length of the hypotenuse.

$\mathrm{AB}^{2}=\mathrm{BD}^{2}+\mathrm{AD}^{2}$

$\begin{array}{l}{a^{2}=\left(\frac{a}{2}\right)^{2}+(4 \sqrt{3})^{2}} \\\\ {a^{2}-\left(\frac{a}{2}\right)^{2}=(4 \sqrt{3})^{2}}\end{array}$

$\frac{4 a^{2}-a^{2}}{4}=16 \times 3$

$\begin{array}{l}{\frac{3 a^{2}}{4}=16 \times 3} \\\\ {3 a^{2}=192} \\\\ {a^{2}=192 \div 3=64}\end{array}$

a = 8

Hence, the three sides of the triangle are 8 units each

In equilateral traingle, length of all three sides of triangle are equal

So, Perimeter = 3 $\times$ (Length of each side of triangle)

Perimeter = 3 $\times$ 8 = 24

Thus the perimeter of the equatorial triangle is 24 units

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3 years ago

Mix some of the $5.50 per pound with 100 pounds of $6.25 per pound to get a $6 per pound mix

Dvinal [7]

x lbs * 5.5 + 100 lbs * 6.25 = (x+100) * 6.00

distribute

5.5x + 625 = 6x+600

subtract 5.5 x from each side

625 = .5x +600

subtract 600 from each side

25 = .5x

divide each side by .5

x = 100

You need 100 pounds of the 5.50 mix

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3 years ago

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