Problem: In the figure below, AB is perpendicular to BC and DD = DC. If AD =$\sqrt{10}$ cm and AC = 4 cm, then what is the value of BC?
View all: BANGLADESH KRISHI BANK | SENIOR OFFICER | WRITTEN MATH QUESTION SOLVE | 2011
Correct Answer: $2\sqrt{2}$
Explanation:
Given that, AB $\bot$ BC
BD = DC
AD = $\sqrt{10}$
AC=4
Since AB $\bot$ BC
So, AB² + BC² = AC²
AB² + (BD + CD) = AC² [°.’ BC = BD + CD]
AB² + (BD + CD) = AC² [ BC = DC]
AB² + 4BD² = AC²
(AB² + BD²) + 3BD² = AC²
AD² + 3BD² = AC² [AB² + BD² = AD²]
($\sqrt{10}$)² + 3BD² = AC²
10 + 3BD² = 16
3BD² = 6
BD = $\sqrt{2}$
BC=BD=CD
BC=BD+BD [BD=DC]
BC=2BD
BC=$2\sqrt{2}$ [BD=$\sqrt{2}$]
