Question

in triangle abc A =90 AN perpendicular Bc BC =12 AC=5 Find the ratio of the area of triangle ANC AND triangle ABC​

Answer 1

It is given in ∆ABC,

∠B = 90° ….. (i)

BC = 5 cm

AC = 12 cm

BM ⊥ AC

∴ ∠BMC = ∠BMA = 90° …. (ii)

Now, consider ∆BMC & ∆ABC,

∠C = ∠C ….. [common angle]

∠B = ∠BMC = 90° …… [from (i) & (ii)]

∴ By AA similarity, ∆BMC ~ ∆ABC

Since the ratio of the area of two similar triangles is equal to the square of ratio of their corresponding sides.

∴ [Area of ∆BMC] / [Area of ∆ABC] = []² = []² =

Thus, the ratio of areas of ∆ BMC and ∆ABC is 25:144.