Question

QSRT is a parallelogram with diagonals QS— and RT— intersecting at point A. if RT—=x+15 and RA—=2x+3, what is the length of RT—?

Answer 1

Length of RT is, 18 units.

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,
`a\cdot (b+c) = a\cdot b + a\cdot c`

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;

`(9)/(3) =(3x)/(3)`

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