Question

plz give the proper answer for the below question

Answer 1

Answer: (b) 12m and 5m

Step-by-step explanation:

Let the distance of gate 1 to pole be x

distance of gate 2 to pole be y

Since the park constitute a circle and the pole is contracted on the boundary, we can simply solve this problem by using the following rule.

"Angles formed by drawing lines from the ends of the diameter of a circle to its circumference form a right angle."

So d = 13m, OP = x, AD = y

Pythagoras theorem,

Hyp² = Op² + Ad²

169 = x² + y²

Also given,

x - y = 7 ----------(1)

(x - y)² = 7²

x² + y² - 2xy = 49

169 - 2xy = 49

2xy = 120

xy = 60

y = 60/x

sub y in (1)

x - 60/x = 7

x² - 60 = 7x

x² - 7x - 60 = 0

(x - 12)(x + 5) = 0

x = 12 or x = -5. x= -5 is not possible. distance can't be negative

sub x = 12 in (1)

y = 12 - 7

y = 5

x = 12, y = 5

Thank you.