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
2.6
To find the length of line RT, we first need to determine the length of line QS since it forms a diagonal of rhombus PQRS.
Since PSQR is a rhombus, the diagonals are equal in length. Thus, we have:
PQ = QR = RS
Given that PQ = (7b - 5) meters and QR = (2b - 0.5) meters, we can set up the following equation:
(7b - 5) = (2b - 0.5)
Solving the equation:
7b - 5 = 2b - 0.5
subtracting 2b from both sides:
7b - 2b - 5 = -0.5
combining like terms:
5b - 5 = -0.5
adding 5 to both sides:
5b - 5 + 5 = -0.5 + 5
simplifying:
5b = 4.5
dividing both sides by 5:
5b / 5 = 4.5 / 5
simplifying:
b = 0.9
Now that we have the value of b, we can substitute it back into the expressions for PQ and QR:
PQ = (7b - 5) = (7 * 0.9 - 5) = 6.3 - 5 = 1.3 meters
QR = (2b - 0.5) = (2 * 0.9 - 0.5) = 1.8 - 0.5 = 1.3 meters
Since PQ = QR = 1.3 meters, we can conclude that the length of line QS is 1.3 meters.
Since S is the midpoint of line RT, we can deduce that QS is equal in length to RT.
Therefore, the length of line RT is 1.3 meters.
To find the length of line RT, we first need to understand the properties of a rhombus.
In a rhombus, opposite sides are parallel, and opposite angles are equal. Additionally, the diagonals of a rhombus bisect each other at right angles.
In this case, we are given that S is the midpoint of line RT. Since R and T are vertices of the rhombus PQRS, line ST is a diagonal of the rhombus. Therefore, line RS must also be a diagonal of the rhombus.
Since RS is a diagonal, it bisects line PT. So, both segments RP and PS are equal in length, forming two congruent right triangles: RPQ and PSQ.
Now, let's calculate the length of line RT using the given information: PQ = (7b-5) meters and QR = (2b-0.5) meters.
Since RP and PS are congruent, we can write the following equation:
PQ + QR + RP + PS = 0
Substituting the given lengths, we get:
(7b-5) + (2b-0.5) + RP + RP = 0
Combining like terms, we have:
9b - 5.5 + 2RP = 0
Solving for RP, we get:
2RP = 5.5 - 9b
RP = (5.5 - 9b) / 2
Since S is the midpoint of line RT, we know that RS = ST. Therefore, we can replace RP with (5.5 - 9b) /2 to find ST:
ST = 2 * RP
= 2 * [(5.5 - 9b) / 2]
= 5.5 - 9b
Thus, the length of line RT is 5.5 - 9b meters.