the sides of a triangular plot are in the ratio3:5:7 and its perimeter is300m.find it’s area​

2 thoughts on “the sides of a triangular plot are in the ratio3:5:7 and its perimeter is300m.find it’s area​”

1. Answer:

   900√10m²

   Step-by-step explanation:

   Let the sides be 3x, 5x and 7x respectively. Perimeter=3x+5x+7x=300

   15x=300

   :.x=20

   3x=60, 5x=100 and 7x=140

   now, semi-perimeter=300/2=150

   Area of ∆=√s(s-a)(s-b)(s-c)

   =√150(150-60)(150-100)(150-140)

   =√150(90)(50)(10)

   =√8100000

   =900√10m²

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2. Solution:-

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   [tex]\large\to{\underbrace{\underline{\sf{Understanding\:the\:concept:-}}}}[/tex]

   ⟹ Here it is given in the question that the perimeter of triangular plot is 300 m and its sides are in the ratio 3:5:7. Now, the question has asked us to find out the area of the plot. So, to find the area first of all we need to find out the sides. So, for that we will assume the sides as 3x, 5x and 7x. And after that by following the steps, mentioned below we will get our answer.

   ANSWER:-

   ⬤ 1st side = 60 m

   ⬤ 2nd side = 100 m

   ⬤ 3rd side = 140 m

   ⬤ The area of triangular plot is 1500√3m².

   GIVEN:-

   ⟼ Ratio of sides = 3:5:7

   TO FIND:-

   ⟿ Area = ?

   FORMULA:-

   ➜ Area = √s(s-a)(s-b)(s-c) (Herons formula)

   SOLVING STEP BY STEP:-

   ⟼ Let 1st side = 3x

   ⟼ Let 2nd side = 5x

   ⟼ Let 3rd side = 7x

   ➜ 1st side + 2nd side + 3rd side = Perimeter

   • Finding the number:-

   Perimeter is 300 m.

   So,

   ➜ 3x + 5x + 7x = 300

   Adding the terms:- 3x + 5x + 7x = 15x

   So,

   ➜ 15x = 300

   Transposing 15 to R.H.S:- 300 / 15

   So,

   ➜ x = 300 / 15

   Dividing the terms:- 300 / 15 = 20

   So,

   ➜ x = 20

   Final Answer:- 20

   So,

   ➜ x = 20

   • Sides:-

   ➜ 1st side = 3x

   ⠀⠀⠀⠀⠀3x = 3 × 20

   ⠀⠀⠀⠀⠀⠀⠀= 60

   1st side is 60 m.

   ➜ 2nd side = 5x

   ⠀⠀⠀⠀⠀⠀5x = 5 × 20

   ⠀⠀⠀⠀⠀⠀ ⠀= 100

   2nd side is 100 m.

   ➜ 3rd side = 7x

   ⠀⠀⠀⠀⠀7x = 7 × 20

   ⠀⠀⠀⠀⠀⠀⠀= 140

   3rd side is 140 m.

   VERIFICATION:-

   ➜ 60 + 100 + 140

   ➜ 160 + 140

   ➜ 160 + 140 = 300

   ➜ 300

   300 = 300

   ∴ L.H.S = R.H.S

   Hence, verified.

   How to find the area:–

   • To find the area first of all we have to find out the semi perimeter of the triangle.

   ➜ Semi Perimeter = 1st side + 2nd side + 3rd side / 2

   • Finding the semi perimeter:–

   ➜ Semi Perimeter = 60 + 100 + 140 / 2

   ➜ Semi Perimeter = 300 / 2

   ➜ Semi Perimeter = 300 / 2 = 150

   ➜ Semi Perimeter = 150 cm.

   • Now we need to apply the herons formula in order to find out the area.

   ➜ Herons formula = √s(s-a)(s-b)(s-c)

   • Finding the area:–

   ➜ Area = √150 (150 – 60) (150 – 100) (150 – 140)

   ➜ Area = √150 (90) (50) (10)

   ➜ Area = √150×90×50×10

   ➜ Area = √150×90×50×10 = √6750000

   ➜ Area = √6750000

   ➜ Area = √6750000 = 1500√3m²

   ➜ Area = 1500√3m²

   Thus, we got the answer. The area of triangular plot is 1500√3m².

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