Question

In the given figure, BC ⊥ AB, AD ⊥ AB, BC = 4, AD = 8, then find `("A"(∆"ABC"))/("A"(∆"ADB"))`

Answer 1

In ∆ABC and ∆ADB,
BC ⊥ AB, AD ⊥ AB, BC = 4, AD = 8   ...(Given)

∆ABC and ∆ADB have same base AB. ...(Given)

∴ Areas of triangles with equal bases are proportional to their corresponding heights.

`("A"(∆"ABC"))/("A"(∆"ADB")) = "BC"/"AD"`

∴ `("A"(∆"ABC"))/("A"(∆"ADB")) = 4/8`

∴ `("A"(∆"ABC"))/("A"(∆"ADB")) = 1/2`.