Question

Find the area of a triangular field whose sides are 91 m, 98 m and 105 in length. Find the height corresponding to the longest side.​

Answer 1

Step-by-step explanation:

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Answer 2

GivEn:

• Sides of a triangular field = 91 m, 98 m and 105 in length

To find:

• Area of the triangular feild?

Solution:

• Here, Firstly let's find semi perimeter of the triangle. Then, We'll put the value of it in the herons formula to find area.

• Let height be h m.

« Now, Finding semi perimeter,

⇒ S = a + b + c/2

⇒ 91 + 98 + 105/2

⇒ 294/2

⇒ 147

∴ Hence, Semi perimeter of the triangle is 147.

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« Now, By using herons formula,

We know that,

★ √s(s - a)(s - b)(s - c)

⇒√147(147 - 91)(147 - 98)(147 - 105)

⇒√147(56)(49)(42)

⇒4116 m²

∴ Hence, Area of the triangular field is 4116 m².

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« Now, Let's find height,

As we know that,

• Area = 1/2bh

⇒1/2 × 105 × h = 4116

⇒52.5h = 4116

⇒h = 4116/52.5

⇒h = 78.5 m

∴ Hence, Height of the triangular field is 78.5 m.

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More to know:

• Area of triangle = ½ × base × height

• Heron's Formula = √s(s - a)(s - b)(s - c)

• Sum of all angles of a triangle is 180°.