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How do you find the perimeter of a right angle triangle when its height is 2.4 cm greater than its base and has an area of 34.56 square cm?
Wiki User
∙ 13y ago
In order to find the perimeter the height, base and hypotenuse must be found first so let the height be (x+2.4) and the base be x:
1/2*height*base = area
1/2*(x+2.4)*x = 34.56
Multiply both sides by 2 and multiply out the brackets:
x2+2.4x = 69.12
Subtract 69.12 from both sides thus forming a quadratic equation:
x2+2.4x-69.12 = 0
Solving the above equation by means of the quadratic equation formula gives x a positive value of 7.2
Therefore: height = 9.6 cm and base = 7.2 cm
Use Pythagoras' theorem to find the hypotenuse:
9.62+7.22 = 144 and the square root of this is 12
Therefore: hypotenuse = 12 cm
Therefore: perimeter = 9.6+7.2+12 = 28.8 cm
Wiki User
∙ 13y ago
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