Answer: The answers are in the steps please look carefully.
Step-by-step explanation:
In this given situation, the length of RS plus the length of ST will equal to the length of RT because RS and ST lies on RT. We are given that RS is equal to 2x + 10 and ST is equal to x- 4 , this means that 2x + 10 plus x-4 will equal to 21 because the whole length of RT is 21.
A. Equation: (2x + 10 ) +(x -4) = 21
Now solve the equation for x.
2x + 10 + x -4 = 21 First combine like terms on the left side.
3x + 6 = 21 Subtract 6 from both sides
-6 -6
3x = 15 Divide both sides by 3
x = 5
The value of x is 5.
The length of RS is 2x +10 so since we know the value of x input it into the expression and solve for the real length.
2(5) + 10
10 + 10 = 20
ST is also x -4 so input the value for x and solve for the real length.
5 - 4 = 1
x = 5 , RS = 20 , ST = 1
B. The same applies to B.
RS plus ST has to Equal to RT.
We know the length of RS is 3x -16 and the length of ST is 4x -8 so it has to equal 60.
Equation: ( 3x -16) + (4x - 8) = 60 Solve for x
3x - 16 + 4x -8 = 60
7x - 24 = 60
+24 +24
7x = 84
x= 12
Input 12 in for x and solve for the real lengths
RS = 3(12) - 16
RS = 36 - 16
RS = 20
ST= 4(12) - 8
ST= 48 - 8
ST= 40
x = 12, RS = 20, ST = 40
