Question

learning target: i can apply the segment addition postulate to find the length of a miss.

1. point s is between r and t on $overline{rt}$. rs = 2x - 8, st = 3x - 10, rt = 17. find rs and rt.

given: point s lies between r and t on $overline{rt}$, rs = 2x - 4, st = 8, rt = x + 11. find: rs and rt.
you are hanging four championship banners on a beam across your schools gym. the banners are each 8 ft. wide. the beam is 108 ft. long. you want an equal amount of space between each pair of banners. the distance between the banners and the ends of the beam should be 12 feet less than the space between each pair of banners. how far apart should the banners be placed along the beam?
you are hanging four championship banners on a beam across your schools gym. the banners are each 7.5 ft. wide. the beam is 70 ft. long. you want an equal amount of space between each pair of banners. the distance between the banners and the ends of the beam should be 10 feet less than the space between each pair of banners. how far apart should the banners be placed along the beam?
you are hanging four championship banners on a beam across your schools gym. the banners are each 13.5 ft. wide. the beam is 189 ft. long. you want an equal amount of space between each pair of banners. the distance between the banners and the ends of the beam should be 20 feet less than the space between each pair of banners. how far apart should the banners be placed along the beam?

Explanation:

Step1: Apply segment - addition postulate

Since point $S$ is between $R$ and $T$ on $\overline{RT}$, we have $RS + ST=RT$. Given $RS = 2x - 8$, $ST = 3x - 10$, and $RT = 17$, we substitute these into the equation: $(2x - 8)+(3x - 10)=17$.

Step2: Simplify the left - hand side

Combine like terms: $2x+3x-8 - 10=17$, which gives $5x-18 = 17$.

Step3: Solve for $x$

Add 18 to both sides of the equation: $5x-18 + 18=17 + 18$, so $5x=35$. Then divide both sides by 5: $x=\frac{35}{5}=7$.

Step4: Find $RS$

Substitute $x = 7$ into the formula for $RS$: $RS=2x - 8=2\times7 - 8=14 - 8 = 6$.

Step5: Confirm $RT$

We already know $RT = 17$.

Step1: Expand the equation

$2x-24 + 3x+32 = 108$.

Step2: Combine like terms

$2x+3x-24 + 32=108$, which gives $5x + 8=108$.

Step3: Solve for $x$

Subtract 8 from both sides: $5x+8 - 8=108 - 8$, so $5x = 100$. Then divide both sides by 5: $x = 20$.

Answer:

$RS = 6$, $RT = 17$

For the banner - hanging problem:
Let the distance between each pair of banners be $x$ feet.
The total length of the 4 banners is $4\times8=32$ feet.
The distance between the banners and the ends of the beam is $x - 12$ feet. There are 2 such end - distances and 3 spaces between the 4 banners.
The length of the beam is 108 feet. So we can set up the equation: $2(x - 12)+3x+32 = 108$.