Question

In the given figure, ∠ABC = 90°, AC = 13 cm, CD = 11 cm, AD = 20 cm. Find BC and AB.

Answer 1

Given,

In the given figure, ∠ABC = 90°, AC = 13 cm, CD = 11 cm, AD = 20 cm

In triangle ABC.

Let AB = x and BC = y

ΔABC is right angle triangle, right angle at C.

AC² = AB² + BC²

13² = x² + y²

169 = x² + y² or x² + y² = 169   ...(i)

In triangle ABD,

AC² = AB² + BD²

20² = x² + y + 11²

20² = x² + y² + 2 × y × 11 + 11²

400 = x² + y² + 22y + 121

x² + y² = 400 – 121 – 22y

x² + y² = 279 – 22y   ...(ii)

In ii Substituting x² + y² for 169 from i,

169 = 279 – 22y

110 = 22y

y = 5 cm

Therefore, BC = y = 5 cm

Substitute the value of y in equation i,

x² + y² = 169

x² + 25 = 169

x² = 169 – 25

x =`sqrt(144)`

x = 12 cm

Therefore, AB = x = 12 cm

Hence, BC = 5 cm, AB = 12 cm.