Question

In $\Delta ABC,AN\perp BCandBM\perp AC$ if $AC=8cmandBC=7.5cm$, If $AN=8.0cm$, and length of $BM$ is given by $\frac{p}{q}$, where p and q are co-primes, then find the value of $p-7q$.

Answer 1

In triangle $ANC$ and $BCM$
$\angle ANC=\angle BMC$
$\angle ACB=\angle ACN$
$△ANC\sim △BCM$
So,

$\frac{AC}{AN}=\frac{BC}{BM}$

$\frac{8}{8}=\frac{7.5}{BM}$

$BM=7.5cm=\frac{15}{2}cm=\frac{p}{q}$

$p=15,q=2$

$p-7q=15-7\times 2=1$