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What are the lengths of each diagonal of a rhombus when they add up to 11.55 cm and it has an area of 16.335 square cm showing all work with answers?
Wiki User
∙ 8y ago
Let the diagonals be x and y and so:-
If: x+y = 11.55 then y = 11.55-x
Area: 0.5*x*y = 16.335 => x*(11.55-x) = 16.335*2
So: 11.55x-x^2 = 32.67 => 11.55x-x^2 -32.67 = 0
Solving the above quadratic equation: x = 4.95 or x = 6.6
Therefore by substitution its diagonals are: 4.95 cm and 6.6 cm
Check: 4,95+6.6 = 11.55 cm which is the sum of its diagonals
Check: 0.5*4.95*6.6 = 16.335 square cm which is its area
Wiki User
∙ 8y ago
Wiki User
∙ 8y agoYou can solve the following two simultaneous equations.1) For the sum of the diagonals: L + W = 11.55
2) For the area: LW/2 = 16.335
One way to do this is to solve the first equation for "L", then replace that in the second equation.
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What is the area of a rectangle whose dimensions are in the ratio of 5 to 12 with a diagonal of 17.55 cm showing all aspects of work?
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