Răspuns:
Explicație pas cu pas:
a)
CE⊥BC
DF⊥BC
cos∡B= 0,6= 6/10= 3/5
cos ∡B= cateta alaturata (BE) / ipotenuza (BC)=3/5
BE= 3x
BC= 5x =CD= AD
BC= 5x
CD=5x
AD=5x
AB= AF+ EF+ EB= 3x+5x+3x=11x
11x= 88
x= 88:11
x= 8 cm
BC= 5*8=40 cm
CD=40 cm
AD= 40 cm
-
deci CD= 40 cm
-
b)
Δ BCE- ∡E=90°
- CE²=BC²-BE²
- CE²= 40²-24²
CE²= 1600-576
CE²=1024
CE²=√1024
CE²=32 cm
-
Δ ACE - AE= AB-EB=88-3 *8= 88-24= 64 cm
AC²=AE²+CE²=64²+32²=32²*2²-32²*1=32²(2²-1)
AE²=32²*3
AE=32√3cm
BD= 32√3 cm
-
c)
A ABCD =[ (B+b) *h]/2
A ABCD= [ AB+DC)*CE ]/2
A ABCD= [(88+40)*32 ]/2
A ABCD= (128*32)/2
A ABCD= 128*16
A ABCD= 2048 cm²
