190 = x + 2(x+20)
190 = x + 2x + 40
190 = 3x + 40
190 - 40 = 150
150/3 = 50
x = 50
190 = 50 + 2(50 + 20)
one side of the width (the "short side", as it says) is the barn, so you don't count that because its only asking for the fencing. the length (which would be the long side, which implies that theres only one short side, if that confused you at all) is 20m longer. we figured out that 50m is the width so if both sides are 20m longer, the dimensions of the fencing would be:
50m + 70m + 70m
This is an equilateral triangle, which is a triangle that has 3 congruent/equal sides and 3 congruent angles.
To find "x", you can set the sides equal to each other because they are suppose to be the same length (you can just do two sides because all of the sides are the same)
[Side AB = Side BC]
4x - 10 = 3x + 2 Subtract 3x on both sides
x - 10 = 2 Add 10 on both sides
x = 12
[proof]
Side AB:
4x - 10 Plug in 12 for x
4(12) - 10 = 48 - 10 = 38
Side BC:
3x + 2 Plug in 12 for x
3(12) + 2 = 36 + 2 = 38
Side AC:
5x - 22 Plug in 12 for x
5(12) - 22 = 60 - 22 = 38
This is also an equilateral triangle (the tick marks show that the sides are the same)
A triangle is 180°. So the three angles add up to 180°.
Since this is an equilateral triangle, all the angles should be the same.
Each angle is 60°
[60° + 60° + 60° = 180° or you could have divided 180 by 3 = 60]
Now that you know each angle is 60°, you can do:
(2x - 4)° = 60°
2x - 4 = 60 Add 4 on both sides
2x = 64 Divide 2 on both sides
x = 32
Answer:
Is the highest point of the arch
4×12=48 so it would be 48