We know that the perimeters of similar polygons have the same ratio as any two corresponding sides. Since we are dealing with equilateral triangles, we only need to find the scale factor because we know that in general, the ratio of the area of two similar figures is the square of the scale factor.
Let A1 = 75 and A2 = 27. So we have,
A1/A2 = 75/27 = 25/9
Thus, the scale factor or the ratio of any two sides or the ratio of perimeters of the two triangles is √25/√9 = 5/3.
Or find the side length of each equilateral triangle.
In a triangle A = bh/2.
Since we are dealing with equilateral triangles, we denote the bases of the triangles with 2x1 and 2x2, and the heights with x1√3 and x2√3. So that P1/P2 = 2x1/2x2 = x1/x2.
Let's find these side lengths.
A1 = b1h1/2 (replace A1 with 75, b1 = 2x1 and h1 =x1√3)
75 = (2x1)( x1√3)/2
75 = x12√3 (divide both sides by √3)
75/√3 = x12
A2 = b2h2/2 (replace A2 with 27, b2 = 2x2 and h2 =x2√3)
27 = (2x2)( x2√3)/2
27 = x22√3 (divide both sides by √3)
27√3 = x22
Since P1/P2 = x2/x2 also P12/P22 = x12/x22
So that,
P12/P22 = x12/x22
P12/P22 = (75/√3)/(27√3)
P12/P22 = 75/27 (square root of both sides)
P1/P2 = √75/√27 = √(75/27) = √(25/9) = 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.
You calculate the areas of two shapes and then divide one area by the other to find the ratio of their areas.
There is no simple answer. For an equilateral triangle it is 6.9282/s where s is the length of each side. For a square it is 4/s A regular pentagon: 2.9062/s A regular hexagon: 2.3094/s and so on. The ratio for a circle is 2/r where r is the radius. For irregular polygons there is no rule.
The ratio of areas is the square of the ratio of lengths. Ratio lengths = 1 : 2 → ratio areas = 1² : 2² = 1 : 4 → if the lengths are doubled, the areas of quadrupled (multiplied by 4).
If the ratio of similarity is 310, then the ratio of their area is 96100.
It is 0.6046 : 1 (approx).
TriangleA a=90.6 TriangleB a=188.9 90.6/188.9 = .48 I think this is right, not completely sure though.
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.
You calculate the areas of two shapes and then divide one area by the other to find the ratio of their areas.
A median divides any triangle in half.
The ratio of their surface areas is the square of the ratio of the lengths. Since the ratio of the lengths is 4-1, then the ratio of the surface areas is 4^2-1^2 or 16-1.
There is no simple answer. For an equilateral triangle it is 6.9282/s where s is the length of each side. For a square it is 4/s A regular pentagon: 2.9062/s A regular hexagon: 2.3094/s and so on. The ratio for a circle is 2/r where r is the radius. For irregular polygons there is no rule.
The ratio of areas is the square of the ratio of lengths. Ratio lengths = 1 : 2 → ratio areas = 1² : 2² = 1 : 4 → if the lengths are doubled, the areas of quadrupled (multiplied by 4).
The ratio of their perimeters will be 3:1, while the ratio of their areas will be 9:1 (i.e. 32:1)
I guess you mean the ratio of the areas; it depends if the 2 rectangles are "similar figures"; that is their matching sides are in the same ratio. If they are similar then the ratio of their areas is the square of the ratio of the sides.
If the lengths are in the ratio 3:5, then the surface areas are in the ratio 9:25.
If the ratio of similarity is 310, then the ratio of their area is 96100.