M4maths Previous Puzzles

06 Sep 2022 Mensuration

A boy started from one corner of a rectangular park and walks along the adjacent sides to reach opposite corner. If he had walked through a shortest distance diagonally, he could have saved the distance equal to five-sixth of the shortest side a park, then the ratio of a longest side to the shortest side is:

OPtion

1) 28:9
2) 42:15
3) 35:12
4) 19:8
5) 36:11
6) 16:7
7) 10:3
8) 7:2
9) 9:4
10) None of these

Solution

Let the length=x and breadth=y of a rectangular park.
Distance covered, when boy walked along the adjacent sides = (x+y)
Distance along diagonal=√(x² + y²)
According to given condition: (x+y) - √(x² + y²) = (5/6)*y
(6x+y)/6 = √(x² + y²)
Squaring on both sides, (36x² + y² + 12xy)/36 = x² + y²
12xy = 35y²
x/y = 35/12
Correct Option 3)

Correct Option: 3 Best Solution (2)

G.S.Kantharao   2 years AGO

Let l and b are the sides
(l+b)-√(l^2+b^2)=5b/6
6(l+b)-5b=6(√l^2+b^2)
(6l+b)^2=36(l^2+b^2)
36l^2+b^2-12lb=36l^2+36b^2
35b^2-12lb=0
35b=12l
l/b=35/12
l:b=35:12
My option is 3👈

Like? Yes (2) | No   

AAKASH RAWAT   2 years AGO

(l+b)-x=(5/6)b
x+b=(1/6)b
S.B.S
x^2 = (1/6)b^2
applying Pythagoras theoram
and comparing
by
x^2 = l^2 + b^2
l/b = 35× 3 / 36
l/b = 35/ 12

Like? Yes | No