Question

si ABCD es un paralelogreamo

Answer 1

Solución:

Tenemos:
AC = AE + EC
128 = x + 5y + EC
AE = EC
x + 5y = EC
128 = x + 5y + x + 5y
128 = 2x + 10y
64 = x + 5y

BD = BE + ED
120 = 5x - y + ED
BE = ED
5x - y = ED
120 = 5x - y + 5x - y
120 = 10x - 2y
60 = 5x - y

x + 5y = 64
5x - y = 60

x + 5y = 64
5(5x - y) = 5(60)

x + 5y = 64
25x - 5y = 300
--------------------
26x = 364
x = 364 / 26
x = 14

x + 5y = 64
14 + 5y = 64
5y = 64 - 14
5y = 50
y = 50 / 5
y = 10

AE = x + 5y
AE = 14 + 5(10)
AE = 14 + 50
AE = 64
EC = 64

BE = 5x - y
BE = 5(14) - 10
BE = 70 - 10
BE = 60
ED = 60

x = 14
y = 10
AE = 64
EC = 64
BE = 60
ED = 60