Question

SOMEONE PLEASE ANSWER ASAP!! 55 POINTS!!

Answer 1

EG = 16 and FH =22

Explanation:

We know that the diagonals of a parallelogram bisect each other

so 2a = 3b+2

and 2a+3 = 6b-1

We know have a system of equations to solve

2a = 3b+2

2a+3 = 6b-1

Subtract 3 from each side

2a+3-3 = 6b-1-3

2a = 6b -4

Now we can set the 2 equations equal ( 2a = 3b+2 and 2a = 6b -4)

3b+2 = 6b-4

Subtract 3b from each side

3b-3b+2 = 6b-3b-4

2 = 3b-4

Add 4 to each side

2+4 = 3b-4+4

6 = 3b

Divide by 3

6/3 = 3b/3

2 =b

We want to find a

2a = 3b+2

Substitute in b=2

2a = 3(2) + 2

2a = 6+2

2a =8

Divide by 2

2a/2 =8/2

a = 4

Now that we know a and b

EG = 2a + 3b+2

= 2(4) + 3(2)+2

= 8+6+2

= 16

FH = 2a+3 + 6b-1

= 2(4) +3 +6(2)-1

= 8+3+12-1

= 23-1

= 22