In the given figure. DandE trisect BC. then the term 3AC²+5AD² is?
Please explain this sum with steps
Answers
Answer:
8AE^2
Explanation :
Step-by-step explanation:
Given:
Triangle ABC is a right angle triangle ie., tne angle is 90 ¤
Points D and E trisects BC
and divides BC into 3 equal parts .
BD=EB=EC =X
BD=X
BD=BD+DE=X+X =2X
BC=BD+DE+EC=X+X+X=3X
Consider
triangle ABC
by pythagoros theorem
AD²=AB²+BD²
= AB²+X²
now consider traingle ABE
AE²=AB²+BE²
=AB²+(2x)²
=AB²+4x²
consider triangle ABC
AC²=AB²+BC²
=AB²+(3x)²
=AB²+9x²
prove that 8AE²=3 AC²+5AD²
consider only R.H.S
3AC²+5AD²=3(AB²+9x²)+5(AB²+x²)
=3AB²+27x²+5AB²+5x²
=8AB²+32x²
=8(AB²+4x²)
3AC²+5AD2 =8AE²
Hence proved
Is the correct answer
Hope this ans is helpful for you
Step-by-step explanation:
Given:
Triangle ABC is a right angle triangle ie., tne angle is 90 ¤
Points D and E trisects BC
and divides BC into 3 equal parts .
BD=EB=EC =X
BD=X
BD=BD+DE=X+X =2X
BC=BD+DE+EC=X+X+X=3X
Consider
triangle ABC
by pythagoros theorem
AD²=AB²+BD²
= AB²+X²
now consider traingle ABE
AE²=AB²+BE²
=AB²+(2x)²
=AB²+4x²
consider triangle ABC
AC²=AB²+BC²
=AB²+(3x)²
=AB²+9x²
prove that 8AE²=3 AC²+5AD²
consider only R.H.S
3AC²+5AD²=3(AB²+9x²)+5(AB²+x²)
=3AB²+27x²+5AB²+5x²
=8AB²+32x²
=8(AB²+4x²)
3AC²+5AD2 =8AE²
Hence proved