Answer:
Length of RT is, 18 units.
Step-by-step explanation:
Given : QSRT is a parallelogram with diagonals are QS and RT intersecting at point A.
In parallelogram properties:
- Diagonals of a parallelogram bisect each other.
- Also, Diagonal of a parallelogram separates it into two congruent.
Diagonal (RT) = RA +TA
From the parallelogram properties; RA = TA
then:
RT = RA +RA
RT = 2RA
Substitute the given values of RT = x+15 unit and RA =2x+3 unit in above expression we have;
x + 15 = 2(2x+3)
Using distributive property i.e, [tex]a\cdot (b+c) = a\cdot b + a\cdot c[/tex]
x + 15 = 4x + 6
Subtract x from both sides we get;
x +15-x = 4x + 6 -x
Simplify:
15 = 3x + 6
Subtract 6 from both sides we get;
15 - 6 = 3x+6 -6
Simplify:
9 = 3x
Divide both sides by 3 we get;
[tex]\frac{9}{3} =\frac{3x}{3}[/tex]
Simplify:
x = 3
Substitute the value of x in RT we have;
RT = x+15 = 3+15 =18
Therefore, the length of RT is, 18 units
