Answer:
x = 7
42, 35, 7
Step-by-step explanation:
- EG = 5x+7
- EF = 5x
- FG = 2x-7
Point F is on line segment of EG, therefore EG = EF + FG
- 5x + 7 = 5x + 2x - 7
- 2x = 14
- x = 7
Then
- EG = 5*7 + 7 = 42
- EF = 5*7 = 35
- FG = 2*7 - 7 = 7
Answer:
B. 40 meters
Step-by-step explanation:
— Estimating
The rectangle enclosing the path has sides of length 9 m and 14 m, so its perimeter is 2(9+14) = 46 m. The distance covered will be shorter than that.
The distance from A to C is longer than the distance from D to C, so we know the distance will be longer than 2·14+9 = 37 m.
Only one answer choice fits in the range 37 < d < 46.
____
— Detailed calculation
The distance from B to C is the hypotenuse of a right triangle with sides 9 and 12. You will recognize that these side lengths are 3 times the side lengths of a 3-4-5 right triangle, so the hypotenuse distance is 3·5 = 15 meters.
The circuit length is ...
AB +BC +CD +DA = 2 + 15 + 14 + 9 = 40 . . . . meters
Triangle
m<A + m<B + m<C = 180
8x +12 + 5x+14 + <span>2x +4 = 180
15x + 30 = 180
15x = 180 -30
15x = 150
x = 10
m<A </span><span>= 8x +12
</span>m<A = 8(10) +12
m<A = 80 + 12
m<A = 92
answer
m<A = 92
