Question

Let ∆ABC ~ ∆DEF and their areas be, respectively, 64 cm2 and 121 cm2. If EF = 15.4 cm, find BC.​

Answer 1

Given:-

• ΔABC ~ ΔDEF,
• Area of ΔABC = 64 cm²
• Area of ΔDEF = 121 cm²
• EF = 15.4 cm

As we know, if two triangles are similar, ratio of their areas are equal to the square of the ratio of their corresponding sides,

$\frac{ar. ∆abc}{ar. ∆def } = \frac{ {ab}^{2} }{ {de}^{2} }$

$= \frac{AC²}{DF²} = \frac{BC²}{ {EF}^{2} }$

∴ 64/121 = BC²/EF²

⇒ (8/11)² = (BC/15.4)²

⇒ 8/11 = BC/15.4

⇒ BC = 8×15.4/11

⇒ BC = 8 × 1.4

⇒ BC = 11.2 cm

Answer 2

Answer:

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Let ∆ ABC ~ ∆ DEF and their areas be, respectively, 64 cm2 and 121 cm2. If EF = 15.4 cm, then the value of BC is 11.2 cm.

Step-by-step explanation:

We know that the ratio of the areas of two similar triangles is equal to the square of the ratio of their corresponding sides.

Here it is given that ΔABC ~ ΔDEF

Given, EF = 15.4 cm

Therefore, Area of ΔABC / Area of ΔDEF = (BC)2/(EF)2

64 cm2 / 121 cm2 = (BC)2/(15.4)2

(BC)² = [(15.4)2 × 64] / 121

BC = (15.4 × 8) / 11

BC = 11.2 cm