Triangles ABC and DEF are similar.
(iii) If AC = 19 cm and DF = 8 cm, find the ratio of the area of two triangles.
(iv) If area (∆ABC) = 36 cm², area (∆DEF) = 64 cm² and DE = 6.2 cm, find AB.
(v) If AB = 1.2 cm and DE = 1.4 cm, find the ratio of the areas of ∆ABC and ∆DEF.
Answers
SOLUTION:
(iii) Given : ∆ ABC ∼ ∆DEF , AC = 19 cm and DF = 8 cm
We know that the ratio of areas of two similar triangles is equal to the ratio of squares of their corresponding sides.
ar(ΔABC)/ar(ΔDEF) = (AC/DF)²
arΔABC/arΔDEF = (19/8)²
arΔABC/arΔDEF = (361/64)
Hence, arΔABCarΔDEF = (361/64)
(iv) Given : ∆ ABC ∼ ∆DEF , area of (ΔABC) = 36 cm2 , area (ΔDEF) = 64 cm2 and DE = 6.2 cm.
We know that the ratio of areas of two similar triangles is equal to the ratio of squares of their corresponding sides.
ar(ΔABC)/ar(ΔDEF) = (AB/DE)²
36/64 = (AB/DE)²
√36/64 = (AB/DE)
6/8 = AB/6.2
8AB = 6 × 6.2
AB = 37.2/8
AB = 4.65 cm
Hence, the length of AB is 4.65 cm.
(v) Given : ∆ ABC ∼ ∆DEF
AB = 1.2 cm and DE = 1.4 cm.
We know that the ratio of areas of two similar triangles is equal to the ratio of squares of their corresponding sides.
ar(ΔABC)/ar(ΔDEF) = (AB/DE)²
ar(ΔABC)/ar(ΔDEF) =(1.2/1.4)² = (6/7)²
ar(ΔABC)/ar(ΔDEF)= (36/49)
Hence, ar(ΔABC)/ar(ΔDEF) = 36/49
HOPE THIS ANSWER WILL HELP YOU….
(iii)ABC is similar to DEF.So AB/DE=BC/EF=AC/DF=19/8.
Therefore ar (ABC)/ar (DEF)=(AC/DF)^2=(19/8)^2=361/64