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vivado [14]
2 years ago
11

The perimeter of the triangle is 131 inches. Write an equation to find the length labeled x. Then solve the equation

Mathematics
2 answers:
ser-zykov [4K]2 years ago
5 0
Hello!

The perimeter is all of the sides added up. We can write this equation below.

42+30+x=131

We subtract 30 and 42 from both sides.

x=131-30-42
x=131-72
x=59

Therefore, we have x=59.

I hope this helps!
Deffense [45]2 years ago
3 0
Write the equation: x + 42 + 30 = 131

Combine like terms: x + 72 = 131

Subtract 72 from both sides: x = 59
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Answer: 10, 11 and 12.

Step-by-step explanation:

This translates to:

Find the natural numbers of two digits that fulfill the condition that when triple and decreased in 5, is less than the double increased in 8?

suppose that A is our number of two digits, this means that:

3*A - 5 < 2*A + 8

It makes sense to start with the smaller number of two digits, 10.

3*10 - 5 < 2*10 + 8

25 < 28

this is true.

Now let's check the next one, 11.

11*3 - 5 < 2*11 + 8

28 < 30

This is true again, now let's try with the next one, 12.

3*12 - 5 < 2*12 + 8

31 < 32

This is true again, now let's find the last one.

3*13 - 5 < 2*13 + 8

34 < 34

this is not true, so the numbers that fulfill the condition are 10, 11, and 12.

A faster way to prove it is, suppose that both sides of our inequality are equal, then find the value of A.

3*A - 5 = 2*A + 8

3*A - 2*A = 8 + 5 = 13

A = 13

This means that any number of two digits less than 13 fulfills the condition, those numbers are 10, 11, and 12.

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