If one side of a triangle is 7 with its perimeter equal to 18, and area equal to √(108), then the other two sides are:
Show answer & explanation
Correct answer: D
Explanation
The correct answer is option 4 i.e 3 and 8.
| Understanding | Application |
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Let sides of the triangle are a,b and c. a = 7 cm Perimeter of a triangle = ( a + b + c) As we know when sides of a triangle is given then area of triangle is √ s(s - a) (s - b) ( s - c) Where, s is semi perimeter s = ( a + b + c) / 2 = 18/2 = 9 cm |
Area of triangle = √ 108 = √ s(s - a) (s - b) ( s - c) 108 = 9(9 - a) ( 9 - b) (9 - c) 108 = 9 (9 - 7) (9 - b) (9 - c) ... (i) Now as given perimeter is 18 cm. a + b + c = 18 7 + b + c = 18 b + c = 11 c = 11 - b .... (ii) After putting value of c in eq. (i). 108 = 9 (2) (9 - b) ( 9 - 11 + b) 6 = ( 9 - b)( 2 + b) 6 = 9b + 2b - b2 - 18 b2 - 11b + 24 = 0 b(b - 8) - 3(b - 8) = 0 (b - 8)(b - 3) = 0 b = 8, 3 Put the value of b in eq . (ii). c = 11 - 8 = 3 So, other two sides are 8 cm and 3 cm |