Question

Urgent!! In trapezul ABCD, AB||CD, AB=45 cm,BC=20 cm,CD=20cm si AD=15 cm. Aflati inaltimea trapezului si diagonala BD a trapezului.

Answer 1

Ducem inaltimile DE si CF
notam AE cu x
notam BF cu y
si scriem teorema lui Pitagora pentru DE si CF in Δ ADE si Δ CFB
DE² =15²-x²
CF² =20²-y²
x=45-20-y=25-y
DE²= CF²=15²-x²  =20²-y²
225-(25-y)²=20²-y²
225-625+50y-y²=400-y²
50y=800
y=16 cm
x=25-16=9 cm
DE = √(15²-x²)=√(225-81)=√144=12
CF =√(20²-y²) = √(400-256)=√144=12 cm
EB=20+16=36
BD=√(EB²+DE²)=√(36²+12²)=√(1296+144)=√1440=12√10 cm