Question

Q.3. Multiple choice question-
The measure of each side of an equilateral triangle
whose area is 73 cmºis -
(a) 8 cm (b) 2 cm (c) 4 cm (d) 16 cm
​

Answer 1

Given:-

• Area of triangle ,A = 73 cm²

To Find:-

• Side of Equilateral triangle ,a

Solution:-

We know that all side in Equilateral triangle are equal and in Equilateral triangle each angle is 60°.

◍ Area of Equilateral Triangle = √3/4 (side)²

Substitute the value we get.

➨ 73 = √3/4 × (a)²

➨ 73×4 = √3 × a²

➨ 292 = √3×a²

➨ a² = 292/√3

➨ a² = 168.78

➨ a = √168.78

➨ a = 12.99cm ≈ 13cm

Therefore, the side of the equilateral triangle is 13 cm.

Hence, the required answer is 13 cm .

Answer 2

Answer:

Given :-

• The measure of each side of an equilateral triangle whose area is 73 cm.

To Find :-

• What is the area of an equilateral triangle.

Formula Used :-

$\boxed{\bold{\small{Area\: of\: equilateral\: triangle\: =\: \dfrac{\sqrt{3}}{4}\: ×\: {(side)}^{2}}}}$

Solution :-

» Area of an equilateral triangle is 73 cm

➣ According to the question by using the formula we get,

⇒ 73 = $\dfrac{\sqrt{3}}{4}\: ×\: {(side)}^{2}$

By doing cross multiplication we get,

⇒ 4(73) = $\sqrt{3}\: ×\:{(side)}^{2}$

⇒ 292 = $\sqrt{3}\: ×\:{(side)}^{2}$

⇒ (side)² = $\dfrac{292}{\sqrt{3}}$

⇒ (side)² = 168.58

⇒ side = $\sqrt{168.58}$

➠ a = 12.98 ≈ 13 cm

∴ The side of equilateral triangle is 13 cm .

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