Question

A side of an equilateral triangle ABC is 4 cm
Find the side of an equilateral triangle PQR
whose area is double the area of A ABC.

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Answer 1

Answer:

Side of ΔPQR = 4√2 cm

Step-by-step explaination:

Let the side of ΔPQR be s cm.

Area of an equilateral triangle =

$\frac{ \sqrt{3} }{4} \times {(side)}^{2}$

In ΔABC,

Side of ΔABC = 4 cm

Area of ΔABC =

$\frac{ \sqrt{3} }{4} \times {4}^{2} \\ \sqrt{3} \times 4 \\ = 4 \sqrt{3} \: cm$

Given that,

Area of ΔPQR = 2 * Area of ΔABC

$\frac{ \sqrt{3} }{4} \times {s}^{2} = 2 \times 4 \sqrt{3} \\ {s}^{2} = \frac{2 \times 4 \sqrt{3} \times 4 }{ \sqrt{3} } \\ {s}^{2} = 32 \\ s = \sqrt{32} = 4 \sqrt{2} \: cm$

Side of ΔPQR = 4√2 cm

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Answer 2

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