Question

in the given figure ab=9cm bc=12cm and ac is15 cm bp is perpendicular to ac find measure of angle abc prove that triangla apb is similarly to triangle abc ​

Answer 1

$\huge\star\underline\mathfrak\red{Answer:-}$

in Rt∆ when BP is Perpendicular To AC ,

we have ,

\large\red{\boxed{\sf BP²=AP*PC}}

-------------(1)

\Large\bold{\boxed{\boxed{ < /strong > < strong > AB < /strong > < strong > \ < /strong > < strong > : < /strong > < strong > ²\:=\:AP\:×\: < /strong > < strong > A < /strong > < strong > C}}}

-------------(2)

using (2) we get,

9² = AP*15

AP = 81/15(Ans)

PC = 15-(81/15) = 144/15

putting this value in (1) we get,

BP² = (81/15)*(144/15)

BP² = (81*144)/(15)²

BP = 9*12/15 = (36/5) (Ans)

Answer 2

Answer:

in Rt∆ when BP is Perpendicular To AC ,

we have ,

\large\red{\boxed{\sf BP²=AP*PC}}

BP²=AP∗PC

-------------(1)

\Large\bold{\boxed{\boxed{ < /strong > < strong > AB < /strong > < strong > \ < /strong > < strong > : < /strong > < strong > ²\:=\:AP\:×\: < /strong > < strong > A < /strong > < strong > C}}}

</strong><strong>AB</strong><strong> </strong><strong>:</strong><strong>²=AP×</strong><strong>A</strong><strong>C

-------------(2)

using (2) we get,

9² = AP*15

AP = 81/15 (Ans)

PC = 15-(81/15) = 144/15

putting this value in (1) we get,

BP² = (81/15)*(144/15)

BP² = (81*144)/(15)²

BP = 9*12/15 = (36/5) (Ans)

Step-by-step explanation:

hope it will help you

mark me as brainlliest