The scissor lift forms rhombus PQRS with PQ= (7b-5) meters and QR= (2b-0.5) meters. IF S is the midpoint of Line RT, what is the length of line RT
To find the length of line RT, we need to establish the relationship between the given information.
Given:
- PQ = (7b - 5) meters
- QR = (2b - 0.5) meters
We know that PQRS forms a rhombus, which means opposite sides are equal in length. Additionally, we are given that S is the midpoint of line RT.
Since the diagonals of a rhombus bisect each other at right angles, we can conclude that SR is equal in length to SP. Hence, RT is twice the length of SR.
To find SR, we need to calculate SP first.
Let's calculate the lengths of SP and SR:
SP = PQ - PS
= (7b - 5) - (2b - 0.5)
= 7b - 5 - 2b + 0.5
= 5b - 4.5
Since SR is equal to SP, we have SR = SP = 5b - 4.5.
Now, to find the length of line RT, we multiply the length of SR by 2:
RT = 2 * SR
= 2 * (5b - 4.5)
= 10b - 9
Therefore, the length of line RT is 10b - 9 meters.
To find the length of line RT, we first need to determine the length of line QS.
Since the scissor lift forms a rhombus, opposite sides of a rhombus are equal in length. Thus, we have:
PQ = SR
(7b-5) = (2b-0.5)
To solve for b, we can simplify and solve the equation:
7b - 5 = 2b - 0.5
7b - 2b = -0.5 + 5
5b = 4.5
b = 4.5/5
b = 0.9
Now that we have the value of b, we can substitute it back into the equation to find the length of line QS:
PQ = (7b - 5)
PQ = (7(0.9) - 5)
PQ = 6.3 - 5
PQ = 1.3 meters
Since S is the midpoint of line RT,
RS = 0.5 * PQ
RS = 0.5 * 1.3
RS = 0.65 meters
And since the scissor lift forms a rhombus, we know that RQ = RS, so:
RQ = 0.65 meters
Finally, to find the length of line RT, we need to add the lengths of RQ and QT:
RT = RQ + QT
RT = RQ + SR (since S is the midpoint of RT)
RT = 0.65 + 0.65
RT = 1.3 meters
Therefore, the length of line RT is 1.3 meters.