The sacle factor between two shapes is the same as the ratio of their perimeters.
I am not sure what this is?
5:3
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.
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.
Their perimeters are in the same ratio.
The ratio of their perimeters will be 3:1, while the ratio of their areas will be 9:1 (i.e. 32:1)
The sacle factor between two shapes is the same as the ratio of their perimeters.
I am not sure what this is?
4.9
5:3
The ratio of their perimeters is also 45/35 = 9/7. The ratio of their areas is (9/7)2 = 81/63
The ratio is 16 to 81.
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.
is it 3:5 and 3:5
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.
If lengths are in the ratio a:b, then areas are in the ratio a2:b2 since area is length x length. If areas are in the ratio c:d, then lengths are in the ration sqrt(c):sqrt(d). Areas of decagons are 625sq ft and 100 sq ft, they are in the ratio of 625:100 = 25:4 (dividing through by 25 as ratios are usually given in the smallest terms). Thus their lengths are in the ratio of sqrt(25):sqrt(4) = 5:2 As perimeter is a length, the perimeters are in the ratio of 5:2.