Mathematics: 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—?

0=12Step-by-step explanation(5−2)(2−2)=12(3)(2−2)=12...

Qsrt is a parallelogram with diagonals qs— and rt—

diapatil

10.03.2022

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

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;

$\frac{9}{3} =\frac{3x}{3}$

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

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