Answer:
1) x=5. and the sides are: 12, 12, and 12 in length
2) Perimeter = 40
Step-by-step explanation:
Problem 1)
The perimeter of the triangle is the addition of its three sides, and from the information, it should equal 36. So we set an equation for the addition of the three given sides equaling 36:
[tex]3x-3+x+7+2x+2=36\\3x+x+2x-3+7+2=36\\6x+6=36\\6x=36-6\\6x=30\\x=30/6\\x=5[/tex]
Now we can find the length of each side using the obtained value of x (5):
First side: [tex]3x-3 = 3(5)-3=15-3=12[/tex]
Second side: [tex]x+7 = (5) +7=12[/tex]
Third side: [tex]2x+2=2(5)+2=10+2=12[/tex]
Problem 2)
Since we are given the two legs of a right triangle, we can use the Pythagorean theorem to find the length of the hypotenuse (the third side):
side = [tex]\sqrt{15^2+8^2} =\sqrt{225+64} =\sqrt{289} =17[/tex]
So now we can calculate the triangle's perimeter by adding its three sides:
Perimeter= 17 + 15 + 8 = 40
