AB is a tree. At point C two monkeys are sitting.Point D is a well. BC = 5m ,BD =10m. If one monkey comes down to point B and goes to the well . Another comes to point A and directly jumps to point D . If both the distance are equal then find AC and height of the tree
Answers
AC = 2.5 m , Height of Tree = 7.5 ,
Step-by-step explanation:
Distance traveled by monkey who comes doen to B and go to well D
= BC + BD
= 5 + 10
= 15 m
Let say AC = x m
Distance traveled by monkey who goes to A & jump
= AC + AD
= x + AD
x + AD = 15 m
=> AD = 15 - x m
AD² = AB² + BD²
=> (15 - x)² = ( AC + BC)² + BD²
=> 225 + x² - 30x = ( x + 5)² + 10²
=> 225 + x² - 30x = x² + 25 + 10x + 100
=> 100 = 40x
=> x = 2.5
AC = 2.5 m
Height of Tree AB = AC + BC = 2.5 + 5 = 7.5 m
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