In triangle ABC, median AD is on BC and the angle bisector BE (where E lies on AC) are perpendicular to each other. If AD=5cm and BE=7cm and area of triangle ABC=p/q where people and q are coprime then find the sum of digits of p+q
Answers
Answer: In tri. DAE, DE Bisect angle ADB
So we have
DA/DB=AE/EB equ.1
Similarly in tri. DAC, DE Bisect angle ADC
we get
DA/DC=AF/FC
(DC=DB)
DA/DB=AF/FC equ.2
From equ 1 and equ 2
AE/EB= AF/FC
In tri ABC
EF ¶ BE (... BPT)
Given:
ABC is a triangle,
AD is median to BC and BE is perpendicular to AD.
AD=5 cm
BE= 7cm
Area of Triangle ABC = p/q, where p and q are coprimes.
To Find:
Find the sum of digits of p+q.
Solution:
Area of triangle ABD= 1/2×BE×AD
=1/2×7×5
=35/2
Median divides the triangle into two equal areas therefore the area of the triangle ABC = 2×area of the triangle ABD
=2×35/2
=35cm²
As we know area of ABC= p/q
p/q=35/1(p and q are coprimes)
p+q = 35+1
=36
sum of digits of p+q = 3+6
=9
Hence the sum of digits of p+q is 9 .
