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.
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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.
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Step-by-step explanation:
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GivEn:
To find:
Solution:
• 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,
⇒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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