A) 36 cm
B) 32 cm
C) 24 cm
D) 30 cm
Correct Answer: A
Solution :
In \[\Delta ABC,B{{C}^{2}}=A{{B}^{2}}+A{{C}^{2}}\] \[={{(60)}^{2}}+{{(80)}^{2}}=3600+6400=10000\] \[\therefore BC=\sqrt{10000}=100cm\] Area of \[\Delta ABC=\frac{1}{2}\times base\times height\] \[\Rightarrow \frac{1}{2}\times AB\times AC=\frac{1}{2}\times BC\times AH\] \[\Rightarrow \frac{1}{2}\times 60\times 80=\frac{1}{2}\times 100\times AH\] \[\Rightarrow AH=\frac{60\times 80}{100}=48cm\] Now, in \[\Delta ABH,B{{H}^{2}}=A{{B}^{2}}-A{{H}^{2}}\] \[={{(60)}^{2}}-{{(48)}^{2}}=1296\] \[\therefore BH=\sqrt{1296}=36cm\]
You need to login to perform this action.
You will be redirected in
3 sec
