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What are two different size squares that the ratio of their perimeters is the same as the ratio of their areas?
Wiki User
∙ 16y ago
Assume square A with side a; square B with side b. Perimeter of A is 4a; area of A is a2.
Perimeter of B is 4b; area of B is b2. Given the ratio of the perimeters equals the ratio of the areas, then 4a/4b = a2/b2; a/b = a2/b2 By cross-multiplication we get: ab2 = a2b Dividing both sides by ab we get: b = a This tells us that squares whose ratio of their perimeters equals the ratio of their areas have equal-length sides. (Side a of Square A = side b of Square B.) This appears to show, if not prove, that there are not two different-size squares meeting the condition.
Wiki User
∙ 16y ago
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How do scale factor and ratio of perimeters compare?
The sacle factor between two shapes is the same as the ratio of their perimeters.
Ratio of perimeters given ratio of similitude?
They are the same.
How do you solve the ratio perimeters of two smaller squares is 5 to 4 if the area of the smaller square is 32 square units what is the area of the larger square?
The area of similar figures is proportional to the square of any linear measurement. (And all linear measurements are directly proportional.) Thus, if the ratio of the perimeters is 5/4, the ratios of the lengths of sides is also 5/4. The ratio of the areas, on the other hand, is (5/4)2, so you can simply multiply the area of the smaller square by this factor.
What is the ratio 15ft to 9ft of the perimeters?
5:3
An equilateral triangle and a square have equal perimeters what is the ratio of the area of the triangle to the area of the square?
If an equilateral triangle and a square have equal perimeters, then the ratio of the area of the triangle to the area of the square is 1:3.
If the perimeters of two squares are in a ratio of 4 to 9 what is the areas of the two squares?
The ratio is 16 to 81.
Two triangles are similar and have a ratio of similarity of 3 1 What is the ratio of their perimeters and the ratio of their areas?
The ratio of their perimeters will be 3:1, while the ratio of their areas will be 9:1 (i.e. 32:1)
What is the width of two similar rectangles are 45 yd and 35 yd what is the ratio of the perimeters of the areas?
The ratio of their perimeters is also 45/35 = 9/7. The ratio of their areas is (9/7)2 = 81/63
What is the relationship between perimeters and areas of similar figures?
Whatever the ratio of perimeters of the similar figures, the areas will be in the ratios squared. Examples: * if the figures have perimeters in a ratio of 1:2, their areas will have a ratio of 1²:2² = 1:4. * If the figures have perimeters in a ratio of 2:3, their areas will have a ratio of 2²:3² = 4:9.
Is it true that the greater the perimeter the greater the area?
No, in general that is not true. For two similar figures it is true. But you can easily design two different figures that have the same perimeters and different areas, or the same area and different perimeters. For example, two rectangles with a different length-to-width ratio.
What is the ratio of the areas of an equilateral triangle and a circle if their perimeters are same?
It is 0.6046 : 1 (approx).
What is the similarity ratio and the ratio of the perimeters of two regular octagons with areas of 18in2 and 50in2?
is it 3:5 and 3:5
If the ratio of the side lengths of two similar polygons is 31 what is the ratio of the perimeters?
Their perimeters are in the same ratio.
The ratio of the perimeters of two similar squares is 5 to 4. If the area of the smaller square is 32 Square Units what is the area of the larger square?
50
How do scale factor and ratio of perimeters compare?
The sacle factor between two shapes is the same as the ratio of their perimeters.
Ratio of perimeters given ratio of similitude?
They are the same.
Two squares are similar The ratio of a set of sides is 2 and 4 What is the ratio of their areas?
1:2
