Question

If the ratio of three sides of triangle are 3:4:5.If the perimeter of triangle is 60. Find the area of triangle .​

Answer 1

Step-by-step explanation:

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Answer 2

$\huge\mathfrak{\bf{\underline{\underline{Answer \ ⟹}}}}$

Sides Of Triangle Are In Ratio 3:4:5

Perimeter ⟹ 144

Let,

The Sides Of Triangle Be ${3x \ , \ 4x \ , \ 5x .}$

$ㅤㅤㅤㅤㅤPerimeter = 3x + 4x + 5x \\ ㅤㅤㅤ60 = 3x + 4x + 5x \\ 60 = 12x \\ x = 5$

Then Sides Of Triangles Are,

$ㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤ3x = 3(5) = 15$

$ㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤ4x = 4(5) = 20$

$ㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤ5x = 5(5) = 25$

Now,

$Semiperimeter = s = \frac{sum \: of \: sides \: of \: triangle}{2} \\</p><p> Semiperimeter = s = \frac{15 + 20 + 25}{2} \\</p><p></p><p>Semiperimeter = s = \frac{60}{2 } \\ </p><p></p><p>Semiperimeter = s = 30$

USING HERON'S FORMULA,

$AREA \: OF \: TRAINGLE \implies \: ㅤㅤㅤㅤㅤㅤㅤㅤㅤ</strong><strong>ㅤ</strong><strong>ㅤ</strong><strong>ㅤ</strong><strong>ㅤ</strong><strong>ㅤ\sqrt{s(s - a)(s - b)(s - c)}$

$= \sqrt{30(30 - 15)(30 - 20)(30 - 25)} \\ </p><p></p><p> = \sqrt{30(15)(10)(5)} \\</p><p></p><p> = \sqrt{30(750)} \\ </p><p></p><p> = \sqrt{22500} \\ </p><p></p><p>= 150 \: {cm}^{2}$

$ㅤㅤㅤ \boxed{ \boxed{AREA \: OF \: TRAINGLE = 150 { \: cm}^{2} }}$