Question

the ratio of sides of triangle is 4isto4isto 5 if area of triangle is 72 sq units then the length of smallest side is

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Answer 1

Answer:

Answer:Correct Answer:

Answer:Correct Answer:C) 63–√ unit

Answer:Correct Answer:C) 63–√ unitDescription for Correct answer:

Answer:Correct Answer:C) 63–√ unitDescription for Correct answer:3, 4 and 5 from triplet

Answer:Correct Answer:C) 63–√ unitDescription for Correct answer:3, 4 and 5 from tripletLet the sides be 3x, 4x and 5x

Answer:Correct Answer:C) 63–√ unitDescription for Correct answer:3, 4 and 5 from tripletLet the sides be 3x, 4x and 5x⇒12×3x×4x=72

Answer:Correct Answer:C) 63–√ unitDescription for Correct answer:3, 4 and 5 from tripletLet the sides be 3x, 4x and 5x⇒12×3x×4x=72⇒6x2=72

Answer:Correct Answer:C) 63–√ unitDescription for Correct answer:3, 4 and 5 from tripletLet the sides be 3x, 4x and 5x⇒12×3x×4x=72⇒6x2=72⇒x2=12⇒x=23–√

Answer:Correct Answer:C) 63–√ unitDescription for Correct answer:3, 4 and 5 from tripletLet the sides be 3x, 4x and 5x⇒12×3x×4x=72⇒6x2=72⇒x2=12⇒x=23–√∴Smallest side =×23–√=63–√

Answer:Correct Answer:C) 63–√ unitDescription for Correct answer:3, 4 and 5 from tripletLet the sides be 3x, 4x and 5x⇒12×3x×4x=72⇒6x2=72⇒x2=12⇒x=23–√∴Smallest side =×23–√=63–√

Answer 2

Appropriate question: The ratio of sides of a triangle 3:4:5. If area of the triangle is 72 sq units then the length of the smallest side is ?

Given: the ratio of sides of triangle is 3:4:5 & Area of triangle is 72 sq units.

Need to find: Dimensions of triangle & smallest side?

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❍ Let's consider sides of triangle be 3x, 4x & 5x.

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$\sf { \pmb{ S = \dfrac{3x + 4x + 5x}{2} = \dfrac{12x}{2} = 6x }}$

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As we know that,

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$\begin{gathered}\star\:{\underline{\boxed{\frak{ Area_{(triangle)}= \sqrt{s(s - a)(s - b) (s - c) }}}}}\\\\\\ \bf{\dag}\:{\underline{\frak{Putting\:given\:values\:in\:formula,}}}\\\\\\ :\implies\sf \sqrt{6x(6x - 3x)(6x - 4x) (6x - 5x)} = 72\\\\\\ :\implies\sf \sqrt{6x \times 3x \times 2x \times x} = 72\\\\\\ :\implies\sf \sqrt{36 {x}^{4} } = 72 \\\\\\ :\implies\sf {6x}^{2} = 72\\\\\\ :\implies \sf { x }^{2} = \cancel{\dfrac{72}{6}} \\\\\\ :\implies\sf x = \sqrt{12} \\ \\ \\:\implies {\underline{\boxed{\frak{\purple{x = \sqrt[2]{3} }}}}}\:\bigstar\\\\\end{gathered}$

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Therefore,

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Sides of the triangle,

• 3x = 3 × 2√3 = 6√3
• 4x = 4 × 2√3 = 8√3
• 5x = 5 × 2√3 = 10√3

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$\therefore\:{\underline{\sf{Hence,\:The\:smallest\:side\:of\: the\: triangle\: is \:\bf{ \sqrt[6]{3} }\: \sf{respectively}.}}}$