Răspuns:
Explicație pas cu pas:
6) ΔCDM ≈ ΔBER
CDM / BER = 3
CM = 45 cm ; CD = 27 cm ; DM = 36 cm =>
BR = 45:3 = 15 cm ; BE = 27:3 = 9 cm ; ER = 36:3 = 12 cm
15² = 9²+12² = 81+144 = 225 => ΔBER = Δ dreptunghic =>
Aria ΔBER = BE·ER/2 = 9·12:2 = 54 cm²
7) ΔMQP = Δ dreptunghic =>
MN ⊥ PQ ; NP = 2√3 cm ; NQ = 6√3 cm =>
PQ = NP + NQ = 2√3 + 6√3 = 8√3 cm
MN² = NP·NQ = 2√3·6√3 = 12·3 = 36 =>
MN = √36 = 6 cm=>
MP² = MN²+NP² = 6²+(2√3)² = 36+12 = 48 =>
MP = √48 = 4√3 cm
MQ² = MN²+QN² = 6²+(6√3)² = 36+108 = 144
MQ = √144 = 12 cm =>
Perimetrul ΔMQP = MP+MQ+QP = 4√3 cm + 12 cm + 8√3 cm =
= 12√3 cm + 12 cm = 12·(√3 + 1) cm ≈ 32,78 cm
