Question

the lengths of the sides of a triangle are in the ratio 3:4:5and its perimeter is 48cm. find its area​

Answer 1

Answer:

160cm.sq.m

Step-by-step explanation:

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Answer 2

Given that,

• The length of the sides of a rectangle are in the ratio of 3:4:5.

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☯ Let the sides of the rectangle be 3x, 4x & 5x.

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Given that,

• The perimeter of the triangle is 48 cm.

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$:\implies\sf 3x + 4x + 5x = 48 \\\\\\:\implies\sf 12x = 48\\\\\\:\implies\sf x = \cancel\dfrac{48}{12}\\\\\\:\implies{\underline{\boxed{\frak{\pink{x = 4}}}}}$

$\underline{\textsf{Sides \ of \ the \ triangle \ are \ :}}$

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• First side, 3x = 3(4) = 12
• Second side, 4x = 4(4) = 16
• Third side, 5x = 5(4) = 20

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$\therefore\:{\underline{\sf{Hence, \: sides \ of \ the \ \triangle \ are \;\bf{12cm, 16cm \ and \ 20 cm}.}}}$

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⠀⠀⠀$\qquad\quad\boxed{\bf{\mid{\overline{\underline{\purple{\bigstar\: Using \ Heron's \ Formula \ :}}}}}\mid}$⠀

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$:\implies\sf S_{\:(Semiperimeter)} = \dfrac{a + b + c}{2} \\\\\\:\implies\sf S_{\:(Semiperimeter)} = \dfrac{12 + 16 + 20}{2} \\\\\\:\implies\sf S_{\:(Semiperimeter)} = \cancel\dfrac{48}{2}\\\\\\:\implies{\underline{\boxed{\frak{\pink{S_{\:(Semiperimeter)} = 24}}}}}$

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⠀$\star\:\boxed{\sf{\purple{ Area = \sqrt{(s - a) \ (s - b) \ (s - c)}}}}$

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$:\implies\sf Area = \sqrt{24(24 - 12) (24 - 16) (24 - 20)} \\\\\\:\implies\sf Area = \sqrt{24 \times 12 \times 8 \times 4} \\\\\\:\implies\sf Area = \sqrt{9216}\\\\\\:\implies{\underline{\boxed{\frak{\purple{Area = 96 \ cm^2}}}}}\:\bigstar$

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$\therefore\:{\underline{\sf{Hence, Area \ of \ \triangle \ is \;\bf{96 \ cm^2.}}}}$