Question

What time does the area change when sides of a triangle are doubled

Answer 1

Answer:

area becomes 4 times of when sides of a triangle are doubled.

Answer 2

Answer:

4 times

Step-by-step explanation:

Area of triangle when sides are given:

√[s(s-a)(s-b)(s-c)]

when sides are doubled

new a = old 2a

new b = old 2b

new c = old 2c

new s = {old (2a + 2b + 2c) ÷ 2 ÷ old (a + b + c) ÷ 2} × s

= {(a + b + c) × 2 ÷ (a + b + c)} × s

= 2 × s = 2s

New area

√[2s(2s - 2a)(2s - 2b)(2s - 2c)]

= √[2 × s × 2 × (s-a) × 2 × (s-b) × 2 × (s-c)]

= 2 × 2 × {√[s(s-a)(s-b)(s-c)]}

= 4 × {old area}

Therefore, it's 4 times the old area.

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