Q. 34.3( 9 Votes )

# A pole has to be erected at a point on the boundary of a circular park of diameter 13 metres in such a way that the difference of its distances from two diametrically opposite fixed gates A and B on the boundary is 7 metres. Is it the possible to do so? If yes, at what distances from the two gates should the pole be erected?

Answer :

Let the distance of pole from gate A be ‘a’.

Difference of the distance of the pole from two diametrically opposite fixed gates A and B on the boundary is 7 metres.

Distance of pole from gate B = a – 7 m

Diameter of the park = 13 m

Hypotenuse^{2} = length^{2} + breadth^{2}

⇒ 13^{2} = a^{2} + (a – 7)^{2}

⇒ 169 = 2a^{2} + 49 – 14a

⇒ a^{2} – 7a – 60 = 0

⇒ a^{2} – 12a + 5a – 60 = 0

⇒ a(a – 12) + 5(a – 12) = 0

⇒ (a + 5)(a – 12) = 0

⇒ a = 12 m

Thus distance of pole is 12 m from gate A and 5 m from gate B

Rate this question :

The area of a right angled triangle is 165 m^{2}. Determine its base and altitude if the latter exceeds the former by 7 m.

Two squares have sides x cm and (x + 4) cm. The sum of their areas is 656 cm^{2}. Find the sides of the squares.

The perimeter of a rectangular field is 82 m and its area is 400 m^{2}. Find the breadth of the rectangle.

The hypotenuse of a right triangle is 25 cm. The difference between the lengths of the other two sides of the triangle is 5 cm. Find the lengths of these sides.

RD Sharma - MathematicsThe sum of the reciprocals of Rehman’s ages (in years) 3 years ago and 5 years from now is 1/3. Find the present age.

RD Sharma - Mathematics