Question

the area of two similar triangles for 144cm^2 and 324cm^2 if the median of the similar triangle is 16.4cm. find the median of the largest triangle

Answer 1

Answer:

2

Step-by-step explanation:

Answer 2

Solution :-

We know that, when two ∆'s similar ,

• Ratio of their areas = Ratio of square of their corresponding sides .

So,

→ Largest ∆ area / smallest ∆ area = (Largest ∆ side)² / (smallest ∆ side)²

→ 324/144 = (Largest ∆ side)² / (smallest ∆ side)²

→ (18)²/(12)² = (Largest ∆ side)² / (smallest ∆ side)²

→ 18/12 = Largest ∆ side / smallest ∆ side

→ 3/2 = Largest ∆ side / smallest ∆ side .

now, we know that, when two ∆'s similar ,

• Ratio of their corresponding sides = Ratio of their medians .

then,

→ Largest ∆ Median / Smallest ∆ Median = Largest ∆ side / Smallest ∆ side

→ Largest ∆ Median / 16.4 = 3/2

→ 2 * Largest ∆ Median = 16.4 * 3

→ Largest ∆ Median = 8.2 * 3

→ Largest ∆ Median = 24.6 cm (Ans.)

Hence, the median of the largest triangle is equal to 24.6 cm .

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