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!
