PowerPoint Presentation on RATIO
- 1. Prepared by: SABJA RAJAN MOUNT TABOR TRAINING COLLEGE PATHANAPURAM
- 2. Pick out the right angled triangles from the following. Fig. 1 Fig. 2 Fig. 3 Fig. 4 Fig. 5 Fig. 6
- 3. A right angled triangle is shown below. Answer the questions that follows.C A B
- 4. 1)Name the perpendicular sides of the triangle shown? 2)What do we call the third side (BC) of the triangle shown? 3)What is the relation connecting perpendicular sides and hypotenuse of a right angled triangle? 4)What is the area of a triangle? 5)What is the perimeter of a triangle?
- 5. Here comes the problem of the day…
- 6. There are four right triangles, the ratio of perpendicular sides being 3:4 in each. One more fact about each is given below. Find the lengths of the sides of each triangle. i.The difference in the lengths of the perpendicular sides is 24 metres. ii.The hypotenuse is 24 metres. iii.The perimeter is 24 metres. iv.The area is 24 square metres.
- 7. Let’s have a look into the solutions…
- 8. Ratio of the perpendicular sides=3:4 Let the perpendicular sides be 3𝑥 and 4𝑥. By using Pythagoras Theorem, 𝐻𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒2 = (3𝑥)2 +(4𝑥)2
- 9. 𝐻𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒2 = 9𝑥2 + 16𝑥2 = 25𝑥2 ∴ 𝐻𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒 = 25𝑥2 = 5𝑥
- 10. i. Difference in lengths of perpendicular sides=24metres ∴ 𝟒𝒙 − 𝟑𝒙 = 𝟐𝟒 𝒙 = 𝟐𝟒
- 11. ∴ 𝟑𝒙 = 𝟑 × 𝟐𝟒 = 𝟕𝟐 𝟒𝒙 = 𝟒 × 𝟐𝟒 = 𝟗𝟔 𝟓𝒙 = 𝟓 × 𝟐𝟒 = 𝟏𝟐𝟎 ∴ 𝑻𝒉𝒆 𝒔𝒊𝒅𝒆𝒔 𝒂𝒓𝒆 𝟕𝟐𝒎, 𝟗𝟔𝒎 𝒂𝒏𝒅 𝟏𝟐𝟎𝒎.
- 12. ii. 𝑯𝒚𝒑𝒐𝒕𝒆𝒏𝒖𝒔𝒆 = 𝟐𝟒 𝒎 𝒊. 𝒆. , 𝟓𝒙 = 𝟐𝟒 𝒙 = 𝟐𝟒 𝟓 𝒙 = 𝟒. 𝟖
- 13. ∴ 𝟑𝒙 = 𝟑 × 𝟒. 𝟖 = 𝟏𝟒. 𝟒 𝟒𝒙 = 𝟒 × 𝟒. 𝟖 = 𝟏𝟗. 𝟐 𝟓𝒙 = 𝟐𝟒 𝒈𝒊𝒗𝒆𝒏 ∴ 𝑻𝒉𝒆 𝒔𝒊𝒅𝒆𝒔 𝒂𝒓𝒆 𝟏𝟒. 𝟒 𝒎, 𝟏𝟗. 𝟐 𝒎 𝒂𝒏𝒅 𝟐𝟒 𝒎.
- 14. iii. 𝑷𝒆𝒓𝒊𝒎𝒆𝒕𝒆𝒓 = 𝟐𝟒 𝒎 𝒊. 𝒆. , 𝟑𝒙 + 𝟒𝒙 + 𝟓𝒙 = 𝟐𝟒 𝟏𝟐𝒙 = 𝟐𝟒 𝒙 = 𝟐𝟒 𝟏𝟐 𝒙 = 𝟐
- 15. ∴ 𝟑𝒙 = 𝟑 × 𝟐 = 𝟔 𝟒𝒙 = 𝟒 × 𝟐 = 𝟖 𝟓𝒙 = 𝟓 × 𝟐 = 𝟏𝟎 ∴ 𝑻𝒉𝒆 𝒔𝒊𝒅𝒆𝒔 𝒂𝒓𝒆 𝟔𝒎, 𝟖𝒎 𝒂𝒏𝒅 𝟏𝟎𝒎.
- 16. iv. 𝑨𝒓𝒆𝒂 = 𝟐𝟒 𝒎 𝟐 𝒊. 𝒆. , 𝟏 𝟐 × 𝟑𝒙 × 𝟒𝒙 = 𝟐𝟒 𝟏 𝟐 × 𝟏𝟐𝒙 𝟐 = 𝟐𝟒 𝟔𝒙 𝟐 = 𝟐𝟒
- 17. 𝒙 𝟐 = 𝟐𝟒 𝟔 𝒙 𝟐 = 𝟒 𝒙 = 𝟒 = 𝟐
- 18. ∴ 𝟑𝒙 = 𝟑 × 𝟐 = 𝟔 𝟒𝒙 = 𝟒 × 𝟐 = 𝟖 𝟓𝒙 = 𝟓 × 𝟐 = 𝟏𝟎 ∴ 𝑻𝒉𝒆 𝒔𝒊𝒅𝒆𝒔 𝒂𝒓𝒆 𝟔𝒎, 𝟖𝒎 𝒂𝒏𝒅 𝟏𝟎𝒎.
- 19. THANK YOU…