Question

The area of a triangle is 60 square units. If two of its sides are 8 units and 17 units, then the third side is? its urgent pls answer​

Answer 1

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Answer 2

Given :   The area of a triangle is 60 square units.  two of its sides are 8 units and 17 units, then the third side is

To Find : Third Side

Solution:

Let say third side is  x

s = (17 + 8 + x)/2 = (25 + x)/2

Area of Triangle = √((25 + x)/2)((25 + x)/2  - 17))((25 + x)/2  - 8))((25 + x)/2  - x)))

60 = √((25 + x)/2)((x-9)/2)((9 + x)/2  - 8))((25 - x)/2  - x)))

=> 60 = (1/4) √(25² - x²)(x² - 9²)

=> 240 = √(25² - x²)(x² - 9²)

=> 240² = (25² - x²)(x² - 9²)

put x² = y

=> 240² = (25² - y)(y -  9²)

=> 240² =  (625 - y)(y - 81)

=> 57600  = -y² + 706y - 50625

=> y² - 706y  + 108225 = 0

=> (y - 481)(y - 225) = 0

=> y = 481  or y = 225

=> x² = 481   or x² = 225

=> x = √481  or 15

Third side can be √481 ≈ 21.93  cm    or 25 cm

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