Two circles of radii 10 cm and 15 cm respectively are placed inside a square. Find the perimeter of the square to the nearest centimetre

Question

This questions uses Pythagoras theorem and ask about 2 circles in a square and how that will help us find the values of the sides of the square 

 

Answer 1

PROBLEM

 

Two circles of radii 10 cm and 15 cm respectively are placed inside a square. Find the perimeter of the square to the nearest centimetre
This questions uses Pythagoras theorem and ask about 2 circles in a square and how that will help us find the values of the sides of the square

 

SOLUTION

 

THE TWO CIRCLES INSIDE THE SQUARE ARE TANGENT TO ITS SIDES.

 

THE TWO CIRCLES ARE TANGENT TO EACH OTHER.

 

THE DIAMETERS OF THE TWO CIRCLES FORM A 45 DEGREE ANGLE TO THE SIDES.

 

USING 45-45-90 SPECIAL RIGHT TRIANGLES, THE X AND Y VALUES FOR THE 10 CM RADIUS CIRCLE ARE (10√2)/2

 

USING 45-45-90 SPECIAL RIGHT TRIANGLES, THE X AND Y VALUES FOR THE 15 CM RADIUS CIRCLE ARE (15√2)/2

 

THEREFORE, ONE SIDE OF THE SQUARE, s = 10 CM + (10√2)/2 CM + (15√2)/2 CM + 15 CM = 25 + (25√2)/2 CM

 

THE PERIMETER OF THE SQUARE, P = 4s = 4 (25 + (25√2)/2) = 100 + 50√2 CM ≈ 170.7106781 CM ≈ 171 CM