the perimeter of a triangle is 36 cm .if the sum of its two sides is half of the 56cm,find the third side.
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Answer:
Step-by-step explanation:
Sum of Sides = 36 cm,
[math]Base + Perpendicular + Hypotenuse = 36[/math]
Simplifies to,
[math]b + p = 21 [Eqn 1][/math]
For a right triangle,
[math]Base^2 + Perpendicular ^2 = Hypotenuse ^2[/math]
[math]b^2 + p^2 = 15^2 [Eqn 2][/math]
Substitute Eqn 1 in 2,
[math](21 - p)^2 + p^2 = 225[/math]
[math]441 + 2p^2 - 42p = 225[/math]
Reducing it,
[math]p^2 - 21p + 108 = 0[/math]
Solving it gives,
[math]Hence, p = 12 [/math]or[math] 9[/math]
The solution set for the other two sides is [math]{(12,9),(9,12)}[/math]
The difference is thus 3 cms.
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