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What is the area in cm of a rectangle whose diagonal is in the ratio of 13 to 5 to one of its sides while the other side is 78 mm showing work?
Wiki User
∙ 10y ago
Suppose the diagonal is 13k mm and the side is 5k mm.
Then, by Pythagoras, the other side is 12k mm.
Thus 12k = 78 implying that k = 78/12 = 6.5
And therefore, the area is 5k*78 mm2 = (5*6.5) * 78 = 32.5*78 = 2535 mm2.
Another Answer:-
1 Let the diagonal be 13x and the side be 5x
2 Using Pythagoras: (13x)2-(5x)2 = 7.82 because 78 mm = 7.8 cm
3 So: 169x2-25x2 = 60.84 which becomes 144x2 = 60.84
4 Divide both sides by 144 and then square root both sides
5 Therefore: x = 0.65 so diagonal is 13*0.65 = 8.45 and side is 5*0.65 = 3.25
6 Area: 7.8*3.25 = 25.35 square cm
7 Check: 7.82+3.252 = 71.4025 and the square root of this is 8.45 cm which is the length of the rectangle's diagonal
Wiki User
∙ 10y ago
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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
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The two adjacent sides, along with a diagonal make a right angled triangle and so their ratio is the tangent ratio for one of the angles. The two angles are complementary so finding the other is simple.Thus tan(x) = 11.9/15.8 => x = 36.99 deg and so the other angle is 53.01 degrees.
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What are some examples of a ratio?
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What is the diagonal of a square with a side of 10?
14 The ratio of the side of a square to the diagonal is 1.4.
How would you find the answer toA rectangle has a diagonal that measures 20 inches The ratio of the length to the width is 4 to 3 What is the perimeter?
Using Pythagoras' theorem: 162+122 = 400 and the square root of this is 20 (the diagonal) Therefore: 16+12+20 = a perimeter of 48 inches
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?
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
How would you find the two angles created when a diagonal reaches the corner of a rectangle with adjacent side of 15.8 cm and 11.9 cm?
The two adjacent sides, along with a diagonal make a right angled triangle and so their ratio is the tangent ratio for one of the angles. The two angles are complementary so finding the other is simple.Thus tan(x) = 11.9/15.8 => x = 36.99 deg and so the other angle is 53.01 degrees.
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