Question

What is x and the measurements?

Answer 1

x=11

Side lengths:

AB=13

AC=25

BC=37

Explanation:

We can create an equation based off of the given information. Then, we simplify the equation to solve.

`(2x+3)+(3x+4)+(2x-9)=75\\(2x+3x)+(3+4)+(2x-9)=75\\(5x+7)+(2x-9)=75\\(5x+2x)+(7-9)=75\\7x-2=75\\7x=77\\x=11`

Then, we insert 11 for x, and evaluate the expressions for the side lengths.

`AB=2x-9=2*11-9=22-9=13`

`AC=2x+3=2*11+3=22+3=25`

`BC=3x+4=3*11+4=33+4=37`

Finally, we check.

13+25+37 is 75, so this should be correct.

Answer 2

see explanation

Explanation:

The perimeter is the sum of the measures of the 3 sides.

Sum the sides and equate to 75, that is

2x - 9 + 3x + 4 + 2x + 3 = 75, that is

7x - 2 = 75 ( add 2 to both sides )

7x = 77 ( divide both sides by 7 )

x = 11

Thus

AB = 2x - 9 = 2(11) - 9 = 22 - 9 = 13 m

BC = 3x + 4 = 3(11) + 4 = 33 + 4 = 37 m

AC = 2x + 3 = 2(11) + 3 = 22 + 3 = 25 m