# One side of a triangle is 6 cm shorter than the base x. The other side is 4 cm longer than the base. What lengths of the base will allow the perimeter of the triangle to be at least 43cm?

The length of base is 15 cm.

what is Algebra?

A branch of mathematics known as algebra deals with symbols and the mathematical operations performed on them.

Variables are the name given to these symbols because they lack set values.

In order to determine the values, these symbols are also subjected to various addition, subtraction, multiplication, and division arithmetic operations.

Given:

let the base of triangle be x

Length of one side = x- 6

and, length of other side = x+ 4

Now, perimeter of triangle= 43 cm.

x+ x -6 +x +4= 43

3x -2 = 43

3x= 45

x=15

So, x= 15 cm

x-6 = 15- 6 = 9cm

x+ 4 = 15+ 4= 19cm

Hence, the length of base is 15 cm.

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Step-by-step explanation:

x= base

one side= x-6

other side= 4+x

x+x-6+4+x = 43

3x=43+2

x=15 length of base

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Chris Nazarro had total travel expenses of \$872. His transportation cost was \$136. The hotel cost was \$210 and business materials cost \$500. If his lunch cost 30% of his dinner, how much was dinner to the nearest cent?

total travel expenses of \$872
transportation cost was \$136, the hotel cost was \$210 and business materials cost \$500, total of these 3: \$136 + \$210 + \$500 = \$846

\$872 - \$ 846 = \$26

So his lunch and dinner cost \$26
But his lunch cost 30% of his dinner
Lets x is dinner cost
Lunch 30% of dinner cost = 0.3x
x + 0.3x = \$26
1.3x = \$26
x = \$26/1.3
x = \$20

So dinner cost \$20
Lunch: 0.3x = 0.3 (20)  = \$6

There are 4 students and 1/2 sh butcher paper how much paper will each student get