CBSE Class 10 Answered

In the given ΔABC , DE || BC  and  DE / BC = 6/8  .....................(1)

Let us draw a perpendicular line AG from A to BC .

Let AG intersect DE at F. Since DE||BC , AF DE

Area of ΔADE = (1/2) × DE × AF = 45 cm² ( Given )  ............................... (2)

Area of ΔABC = (1/2) × BC × AG  ..........................(3)

Since DE || BC ,  AG / AF = BC / DE = 8/6  ...................... (4)

Using eqn. (1) and (4) , we rewrite eqn.(3) as

Area of ΔABC = (1/2) × (8/6) DE × (8/6) AF = (64/36) × (1/2) × DE × AF ...............(5)

Using eqn.(2) , we rewrite the above expression (5) as

Area of ΔABC =  (64/36) × 45  cm² = 80 cm²