The diagonal of the trapezoid divides the center line into segments. one of which is 5 cm

The diagonal of the trapezoid divides the center line into segments. one of which is 5 cm larger than the other. find the base if the smaller base = 6 cm

Since the AC diagonal divides this trapezoid into two triangles ∆ABS and ∆ACD, the segments KO and ОМ are the midlines of these triangles.

Consider a triangle ABC. Since the KO is parallel to the BC side, its length is equal to half of this side:

KO = BC / 2;

KO = 6/2 = 3 cm.

Consider triangle ACD. Since the length of the OM is 5 cm longer than the length of the KO, then:

OM = KO + 5;

OM = 3 + 5 = 8 cm.

Since the segment OM is parallel to the AD side, its length is equal to half of the AD side:

OM = AD / 2;

AD = OM · 2;

AD = 8 2 = 16 cm.

Answer: the length of the larger base is 6 cm.