Răspuns:
Explicație pas cu pas:
Ducem din C ⊥AB pe care o notam cu E (CE⊥AB)
BE= 36-24
BE=12cm
Δ CEB-∡CEB=90°
- ∡B=60°
- ∡ECB=180- (60+90)=30°
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conform teoremei de ∡=30°
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EB= BC/2
12=BC/2
BC= 12*2
BC= 24 cm
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BE=12 cm
BC= 24 cm
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teorema lui pitagora
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BC²=BE²+EC²
CE²=BC²-BE²
CE²= 576-144
CE²=432
CE=√432
CE= 12√3
CE= AD
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P= 36+24+24+12√3=84+12√3= 12*( 7+√3) cm
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ΔABD -∡A=90°
- AB=36cm
- AD= 12√3
BD²=AB²+AD²
BD²=36²+(12√3)²
BD²=1296+ 432
BD²=1728
BD=√1728
BD= 24 √3 cm ( prima diagonala)
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AC²=AD²+CD²
AC²=432+576
AC²=1.008
AC=√ 1.008
AC= 12√7 cm ( a doua diagonala )
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