ICSE Class 10 Answered

$begin mathsize 12px style In space the space given space figure comma space AB space equals space 14 space cm space and space BC space equals space 18 space cm left parenthesis straight i right parenthesis space Prove space that space triangle ACD space tilde space triangle DCB space space left parenthesis ii right parenthesis space Find space the space length space of space CD. end style$ Please provide solution to this question

Asked by Topperlearning User | 05 Oct, 2017, 08:03: AM

Expert Answer

$begin mathsize 12px style Given colon space AB space equals space 14 space cm comma space BC space equals space 18 space cm therefore space AC space equals space 14 space plus space 18 space equals space 32 space cm space left parenthesis straight i right parenthesis space space space In space triangle ACD space and space triangle DCB comma space space space space space space space angle ACD space equals space angle DCB space left parenthesis Common space angle right parenthesis space space space space space space angle DAC space equals space angle BDC space left parenthesis Alternate space segment space property right parenthesis space space space space space space space therefore space triangle ACD space tilde space triangle DCB space left parenthesis by space AA space similarity right parenthesis left parenthesis ii right parenthesis space space space Now comma space AC over DC equals CD over CB space space space space space space space.... left parenthesis corresponding space sides space of space similar space triangles right parenthesis space space space space space space space space therefore space DC squared equals AC cross times CB equals 32 cross times 18 equals square root of 576 space space space space space space space space therefore space DC equals 24 space cm end style$