Respuesta :

Answer:

a) x = 10

b) DA = 24

c) perimeter = 110

Step-by-step explanation:

a) Since it's a parallelogram, the opposite sides are of equal length. This means that line DC = AB, so u can substitute in the values and solve for x:

DC = AB

5x - 18 = 2x + 12           (move terms so that like terms are on the same side)

5x - 2x = 12 + 18           (simplify like terms)

3x = 30                         (divide by 3 on both sides to isolate the x)

x = 10

b) now that u know the value of x, you can use it to find the length of DA. again, opposite sides are equal, so DA = BC, which means DA = 3x - 6. substitute in your known value of x and solve:

3x - 6

= 3(10) - 6

= 30 - 6

= 24

Therefore, the length of DA - 24

c) Since u know the length of DA (and therefore BC), u just have to find the length of either DC or AB and then multiply that by 2 and add it.

First, substitute in the value of x for either DC or AB (i'm gonna use AB)

2x + 12

= 2(10) + 12

= 20+12

= 32

now, to find the perimeter use this formula: 2(AB) + 2(DA)

this equals to 2(32) + 2(24) = 64+46 = 110

and that's the perimeter!

hope this helps!