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What is the diagonal length of a rectangle whose perimeter is 452.2 mm with an area of 106.134 square cm showing work and answer to an appropriate degree of accuracy if necessary?
Wiki User
∙ 9y ago
Let the dimensions be x, y and change the perimeter into cm:-
Perimeter: 2(x+y) = 45.22 cm => y = 22.61-x
Area: xy = 106.134 => x(22.61-x) = 106.134
So it follows: 22.61x-x^2-106.134 = 0
Solving the above quadratic equation: x = 15.96 or x = 6.65
If: x = 6.65 then y = 15.96
Using Pythagoras: 6.65^2+15.96^2 = 298.9441
Square root of 298.9441 = 17.29 cm or 172.9 mm which is the rectangle's length
Wiki User
∙ 9y ago
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