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What is the length of the diagonal of a rectangle whose dimensions are in the ratio of 3 to 4 with with an area of 369.63 square cm showing work?
Wiki User
∙ 10y ago
Well, you can do your own homework, but here is the general outline of what you must do. Use the variable "x" to express the width of the rectangle. In that case, because of the ratio, the length will be (4/3)x. Write an equation for the area of the rectangle, replace x, (4/3)x and the known area, and solve for "x". (Since a quadratic equation will give you two solutions, you will obviously accept the positive solution.) Once you calculate "x", you can easily calculate the other side of the rectangle, as (4/3)x. Finally, use the Pythagorean Theorem to calculate the diagonal.
Another Answer:-
1 Let the dimensions be 3x and 4x
2 So 3x*4x = 369.63 or 12x2 = 369.63
3 Divide each side by 12 and then square root each side
4 Therefore: x = 5.55 and dimensions must be 16.65 by 22.2
5 Using Pythagoras: 16.652+22.22 = 756.9025 and its square root is 27.75
6 Answer: length of diagonal = 27.75 cm
Wiki User
∙ 10y ago
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