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What are the dimensions of a right angle triangle when its perimeter is 4 times its base with an area of 13.5 square cm showing all aspects of work?
Wiki User
∙ 9y ago
The answer is 4.5 cm, 6.0 cm and 7.5 cm.
This browser has stopped supporting superscripts so I will use sq for squared numbers and sqrt for square roots.
Suppose the three sides are x y and z cm, that the base is x and the other leg is y so that the hypotenuse is z.
Perimeter = 4*x => x+y+z = 4x and therefore y+z = 3x .. .. .. .. (1)
Next, Area = 13.5 sq cm => 0.5*x*y = 13.5,
=> x*y = 27 or y = 27/x and so, substituting for y in (1) gives 27/x + z = 3x
and therefore, z = 3x - 27/x
so that sq(z) = 9*sq(x) - 162 + sq(27/x) .. .. .. .. .. .. .. .. .. .. (2)
Finally, by Pythagoras sq(x) + sq(y) = sq(z)
=> sq(x) + sq(27/x) = sq(z) .. .. .. .. .. .. .. .. .. .. .. .. (3)
Equating (2) and (3)
9*sq(x) - 162 + sq(27/x) = sq(x) + sq(27/x)
=> 8*sq(x) = 162 => sq(x) = 162/8 = 20.25
=> x = sqrt(20.25) = 4.5
Then y = 27/x = 27/4.5 = 6.0
and z = 3x - 27/x = 13.5 - 6 = 7.5
Wiki User
∙ 9y ago
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