SOLUTION: A lot has a frontage of 120 m along the road. The other sides which are both perpendicular to the road are 90 m and 60 m, respectively. It is desired to subdivide the lot into two

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Question 1152805: A lot has a frontage of 120 m along the road. The other sides which are both perpendicular to the road are 90 m and 60 m, respectively. It is desired to subdivide the lot into two by another perpendicular line to the road such that the area of the lot that adjoins the 90-m side is equal to one-third of the whole area. Find the length of the dividing line.
CHOICES:
A. 48.12 m B. 67.92 m
C. 81.24 m D. 97.26 m
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!

let the length of the dividing line be x

x=sqrt%28%28n%2Aa%5E2%2Bm%2Ab%5E2%29%2F%28n%2Bm%29%29...........given a=60, b=90, the 90m side is equal to 1%2F3 of the whole area, then 60m side is equal to 2%2F3, => areas are in 1%3A2 ratio=>n=1 and m=2
x=sqrt%28%281%2A60%5E2%2B2%2A90%5E2%29%2F%281%2B2%29%29
x=sqrt%28%283600%2B2%2A8100%29%2F3%29
x=sqrt%28%283600%2B16200%29%2F3%29
x=sqrt%28%2819800%29%2F3%29
x=sqrt%286600%29
x=81.24

answer:
C. 81.24m