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BabaBlast [244]
3 years ago
13

A triangle has one side length of 12 inches and another of 8 inches. Describe all possible lengths of the third side.

Mathematics
1 answer:
jasenka [17]3 years ago
3 0

Answer:

The possible lengths of the third side is all real numbers greater than 4 inches and less than 20 inches

Step-by-step explanation:

we know that

<u>The Triangle Inequality Theorem</u>. states that the sum of the lengths of any two sides of a triangle is greater than the length of the third side

Let

x -----> the possible lengths of the third side

Applying the Inequality Theorem

1) 12+8 > x

20 > x

Rewrite

x < 20 in

2) 8+x > 12

x> 12-8

x > 4 in

therefore

4 in < x < 20 in

The possible lengths of the third side is all real numbers greater than 4 inches and less than 20 inches

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Let the two numbers are x and y

Let larger number = x

and smaller number = y

it means

x-y = 0.77

Now it says larger number is increased 5 times

So it now becomes 5x

So second equation becomes

5x -y =77

Now we have to solve these two equations

x-y = 0.77 and 5x-y = 77

multiply first equation by -1 and then add both equations

-x+y = -0.77

Now on adding we get

-x+5x +y -y = 77-0.77

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Divide both sides by 4

x=19.0575

We get the larger number , now subtract 0.77 from this , we will get the smaller number

y=19.0575-0.77=18.2875

y=18.2875


Hence the larger number = 19.0575

Smaller number = 18.2875

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2 years ago
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<h3>How to determine the relationship between the trigonometry ratios</h3>

From the question, we understand that:

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The above means that:

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So, the product of the lengths of XY and XZ and the scale factor will result in the lengths of AC and AB,

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Answer:

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