Question

slides of a triangle are in the ratio 12 17 25 and its perimeter 540 cm. find its semi perimeter​

Answer 1

Answer:

Step-by-step explanation:

Ratio of the sides of the triangle = 12 : 17 : 25Let the common ratio be x then sides are 12x, 17x and 25xPerimeter of the triangle = 540cm12x + 17x + 25x = 540 cm⇒ 54x = 540cm⇒ x = 10Sides of triangle are,12x = 12 × 10 = 120cm17x = 17 × 10 = 170cm25x = 25 × 10 = 250cmSemi perimeter of triangle(s) = 540/2 = 270cmUsing heron's formula,Area of the triangle = √s (s-a) (s-b) (s-c)                                       = √270(270 - 120) (270 - 170) (270 - 250)cm2                                       = √270 × 150 × 100 × 20 cm2                                       = 9000 cm2

Answer 2

Appropriate Question:

• Sides of a Triangle are in the ratio of 12:17:15 and it's perimeter is 540 m. Find its semi perimeter.

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☯ Let the sides of the triangle be 12x, 17x and 25x.

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• Here, the perimeter of the given triangle is 540 cm.

Therefore,

$:\implies\sf 12x + 17x + 25x = 540 \\\\\\:\implies\sf 54x = 540 \\\\\\:\implies\sf x = \cancel\dfrac{540}{54} \\\\\\:\implies{\underline{\boxed{\sf{\purple{ x = 10 \ cm}}}}}\:\bigstar$

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• First side, 12x = 12(10) = 120m
• Second side, 17x = 17(10) = 170m
• Third side, 25x = 25(10) = 250 m

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$\therefore\:{\underline{\sf{Hence, \ sides \ of \ the \ triangle \ are \: \bf{120 m, \ 170m \ 250m}.}}}$

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$\dag\:\boxed{\sf{\pink{S_{\:(semi - perimeter)} = \dfrac{a + b + c}{2}}}} \\\\\\:\implies\sf s = \dfrac{120 + 170 + 250}{2} \\\\\\:\implies\sf s = \cancel\dfrac{ 540}{2}\\\\\\:\implies{\underline{\boxed{\frak{\purple{ s = 270 \: cm}}}}}\:\bigstar$

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$\therefore\:{\underline{\sf{Hence, \ semi \ perimeter \ of \ the \ \triangle \ is\: \bf{270 \ cm}.}}}$

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» Now, we'll find area of the triangle too.

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$\dag\:\boxed{\sf{\pink{Area_{\triangle} = \sqrt{s(s - a)(s - b) (s - c)}}}} \\\\\\:\implies\sf Area_{\triangle} = \sqrt{270(270 - 120) (270 - 170) (270 - 250)} \\\\\\:\implies\sf Area_{\triangle} = \sqrt{270 \times 150 \times 100 \times 20} \\\\\\:\implies{\underline{\boxed{\frak{\pink{Area_{\triangle} = 9000\: cm^2}}}}}\:\bigstar$

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$\therefore\:{\underline{\sf{Hence, \ area \ of \ the \ \triangle \ is\: \bf{9000\: cm^2}.}}}$