The difference between the semiperimeter and the sides of a ΔABC are 8cm, 7cm and 5cm respectively.Find the area of the triangle.

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Filo · Accepted Answer

Consider a, b and c as the sides of a triangle and s as the semi perimeterSo we gets - a = 8cms  - b = 7cms - c = 5cmWe know that(s - a) + (s - b) + (s - c) = 8 + 7 + 5On further calculation3s - (a + b + c) = 20We know that a + b + c = 2s3s - 2s = 20So we gets = 20By substituting the value of sa = s - 8 = 20 - 8 = 12cmb = s - 7 = 20 - 7 = 13cmc = s - 5 = 20 - 5 = 15cmWe know thatArea=s(s−a)(s−b)(s−c)​By substituting the valuesArea=20(20−12(20−13)(20−15)​So we getArea=20×8×7×5​It can be written as Area=4×5×4×2×7×5​By multiplicationArea=2014​Therefore, the area of the triangle is 2014​cm2

Question Text	The difference between the semiperimeter and the sides of a $Δ$ ABC are 8cm, 7cm and 5cm respectively.Find the area of the triangle.
Answer Type	Text solution:1
Upvotes	150

The difference between the semiperimeter and the sides of a $Δ$ ABC are 8cm, 7cm and 5cm respectively.Find the area of the triangle.

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