Question

The areas of two similar triangles $\triangle ABC and \triangle DEF$ are 144 $cm^{2}$ and 81 $cm^{2}$ respectively. If the longest side of larger $\triangle ABC$ be 36 cm, then the longest side of the smaller triangle [tex] \triangle DEF [/tex is
(a) 20 cm
(b) 26 cm
(c) 27 cm
(d) 30 cm

Answer 1

Answer:

The length of the longest side of the smaller triangle ∆DEF is 27 cm.

Among the given options option (c) is 27 cm is the correct answer.

Step-by-step explanation:

Given:

ΔABC ~ ΔDEF.

Area of ΔABC = 144 cm ²

Area of ΔDEF = 81 cm².

The longest side(BC) of ΔABC is 36 cm .

Let EF is the longest side of ΔPQR.

ar(ΔABC)/ar( ΔDEF) = (BC/EF)²

[The ratio of area of two similar triangles is equal to the ratio of squares of their corresponding sides.]

144/81 = (36/EF)²

√144/81 = (36/EF)

12/9 = (36/EF)

12 EF = 36 × 9

EF = (36 ×9)/12

EF = 3 × 9  

EF = 27

EF = 27 cm

Hence, the length of the longest side of the smaller triangle ∆DEF is 27 cm.

HOPE THIS ANSWER WILL HELP YOU .

Answer 2

Answer=27 cm

ΔABC congruence to ΔDEF.

Area of ΔABC = 144 cm ²

Area of ΔDEF = 81 cm².

ar(ΔABC)

ar( ΔDEF) = (BC/EF)²

corresponding sides

144/81 = (36/EF)²

√144/81 = (36/EF)

12/9 = (36/EF)

12 EF = 36 × 9

EF = (36 ×9)/12

EF = 3 × 9

EF = 27

EF = 27 cm