Question

ΔABC and ΔEDB are two similar triangles such that BD = `1/2 BC`. If ar(ΔАВC) = 400 cm², find the area (ΔEDB).

Answer 1

Since △ABC ∼ △EDB, the ratio of their areas is equal to the square of the ratio of their corresponding sides.

Given,

`BD = 1/2 BC`

So, `(BD)/(BC) = 1/2`

Thus,

`(ar (ΔEDB))/(ar(ΔАВC)) = ((BD)/(BC))^2`

`(ar (ΔEDB))/400 = (1/2)^2`

`(ar (ΔEDB))/400 = 1/4`

`ar (ΔEDB) = 400 xx 1/4`

ar (ΔEDB) = 100

∴ ar (ΔEDB) = 100 cm²