Question

in a triangle ADE ,BC is parallel to AD .Area of the triangle BCED is 25cm, Area of trapezium BCED=24cm and DE
14cm. Calculate the
length of BC. Also find the area of triangle BCD​

Answer 1

in ∆ABC&∆ADE

as BC//AD corresponding angles are equal.

angleABC = angleADE

angleACB = angleAED

∆ABC is similar to ∆ADE

ar(∆ABC)/ar(∆ADE) = BC^2/DE^2

25/49 = BC^2/ 14^2

BC^2 = 100cm

BC = 10 cm

In trap BCED

area=1/2×sum of parallel sides × h

24=1/2×(10+14)×h

h=48/24

h=2

area of ∆BCD= 1/2 × BC×h

1/2 ×10×2

10cm^2