Find the value of 15 by geometric method.

We have 15 = 3 × 5 . Steps of Construction: (a) Draw a line segment B P and from it cut off a length B D equal to 3 cm and a length D C equal to 5 cm . (b) Taking B C as diameter draw a semicircle. (c) Draw a perpendicular at D on B C which intersects the circumference of the semicircle at A . Then, the line segment A D is the mean proportion of B D and D C . So, A D 2 = B D × D C ⇒ A D = B D × D C ⇒ A D = 3 × 5 cm = 15 cm By scale, we measure and obtain A D = 3 . 9 cm (approx.). Therefore, 15 = 3 . 9 (approx.).

Find the value of 35 by geometric method.

We have 35 = 5 × 7 . Steps of Construction: (a) Draw a line segment B P and from it cut off a length B D equal to 5 cm and a length D C equal to 7 cm . (b) Taking B C as diameter draw a semicircle. (c) Draw a perpendicular at D on B C which intersects the circumference of the semicircle at A . Then, the line segment A D is the mean proportion of B D and D C . So, A D 2 = B D × D C ⇒ A D = B D × D C ⇒ A D = 5 × 7 cm = 35 cm By scale, we measure and obtain A D = 5 . 9 cm (approx.). Therefore, 35 = 5 . 9 (approx.).

Find the value of 2 7 by geometric method.

We know that 2 7 = 4 × 7 . Steps of Construction: (a) Draw a line segment B P and from it cut off a length B D equal to 4 cm and a length D C equal to 7 cm . (b) Taking B C as diameter draw a semicircle. (c) Draw a perpendicular at D on B C which intersects the circumference of the semicircle at A . Then, the line segment A D is the mean proportion of B D and D C . So, A D 2 = B D × D C ⇒ A D = B D × D C ⇒ A D = 4 × 7 cm = 28 = 2 7 cm By scale, we measure and obtain A D = 5 . 3 cm (approx.). Therefore, 2 7 = 5 . 3 (approx.).