Question

 Triangles ABC and DEF are similar.

(i) If area (ΔABC) = 16 cm², area (ΔDEF) = 25 cm² and BC = 2.3 cm find EF.

(ii) If area (ΔABC) = 9 cm² area (ΔDEF) = 64 cm² and DE = 5.1 cm, find AB.

(iii) If AC = 19 cm and DF = 8 cm, find the ratio between the areas of two triangles.

(iV) If area (ΔABC)  36 cm² , area (ΔDEF) = 64 cm² and DE = 6.2 cm, find AB.

Answer 1

(i) We  have 

Answer 2

When two triangles are similar, the ratio of their areas is the square of the ratio of their sides.

1. area (ΔABC) / area (ΔDEF) = BC² / EF² 

⇒16/ 25 = (2.3)²/ EF²
⇒ EF = 2.875 cm

2. area (ΔABC) / area (ΔDEF) = AB² / DE²
⇒9/ 64 = AB² / (5.1)²
⇒ AB = 1.91 cm

3. AC² / DF² = area (ΔABC) / area (ΔDEF)
⇒ area (ΔABC) / area (ΔDEF) = (19)²/ (8)² = 361 : 64

4. area (ΔABC) / area (ΔDEF) = AB² / DE²
⇒ 36 / 64 = AB² / (6.2)²
⇒ AB = 4.65 cm