Are two triangles of equal area and perimeter congruent?

Are two triangles of equal area and perimeter congruent?

Congruent
Please think: after the area is determined (the two points and height of the bottom edge are determined), let the remaining point slide on the line parallel to the bottom edge. Only two symmetrical positions can make the triangle obtain the same perimeter

If the perimeter and area of two triangles are the same, are they congruent?
It's a bit of a problem

Congruent

Are two triangles of equal area and perimeter congruent

As long as an example can be found, it can be overturned
But I'll quote the ocean liner theorem here, with a numerical value as an example
Area s, perimeter L, the sides of the two triangles are ABC OPQ
There is the formula s Square = (L-A) (L-B) (L-C) = (l-o) (L-P) (L-Q) because l is the circumference
Triangle 1: perimeter 18, three sides 8,5,5, area = √ [9 (9-8) (9-5) & sup2;] = 12
Triangle 2: perimeter 18. Three sides 6,6 + √ 33 / 3,6 - √ 33 / 3,
Area = √ [9 (9-6) (9-6 - √ 33 / 3) (9-6 + √ 33 / 3)] = 12
Obviously these two triangles are not congruent
If it's Goldbach's conjecture, then I say this time he's utopian

Two triangles equal perimeter and area, two triangles congruent example, the best picture!
Wrong number, incomplete.

The circumferences are (11,11,4) and (7,7,12) respectively. The two triangles have the same area and the same perimeter but not the same

If the perimeter of a curved triangle is π, what is its area

It is known that the length of each side of a curved triangle is π / 3
Let R be the radius of the circle, then R * (π / 3) = π / 3 and R = 1
Area: 3 π * 1 ^ 2 * [(π / 3) / 2 π) - √ 3 / 2 = π / 2 - √ 3 / 2 = (π - √ 3) / 2

The three sides of a triangle are 50m, 40m and 63m respectively. What is its area

Use Helen's formula: S = √ [P (P-A) (P-B) (P-C)] where p = (a + B + C) / 2
p=(50+40+63)/2=76.5
S=√[76.5*(76.5-50)(76.5-40)(76.5-63)]=√[76.5*26.5*36.5*13.5]=√998927.4375=999.46

The perimeter of a triangle is 11, and the three sides are different integers. Find the area of the triangle

Because the sum of the two sides is greater than the third side, the difference between the two sides is less than the third side, and the perimeter is 11, the three sides are different integers, so the three sides of the triangle can be 2,4,5
According to Helen's formula s = √ [P (P-A) (P-B) (P-C)], where p is half perimeter 11 / 2
a=2,b=4,c=5
Get the triangle area s = √ 11 / 2 (11 / 2-2) (11 / 2-4) (11 / 2-5) = √ (231 / 16) = √ 231 / 4

Please study the relationship between quadrilateral area and perimeter

If you look at a quadrilateral alone, there is no fixed mathematical relationship between area and perimeter,
Compare two quadrilateral, in the case of the same perimeter, the closer the square figure, the larger its area
Compare two quadrilateral with similar shape, the area of perimeter is large, and the area is proportional to the square of perimeter. For example, the perimeter of one quadrilateral is 10, and the other is 20. Then the area of the latter is four times that of the former

Why is the square the largest when a quadrilateral has the same perimeter

I don't need to prove it. Imagine a square box. Whether you open it or flatten it, its area will decrease to zero

For a triangle, the lengths of the three sides are 3 / 5, 3 / 2 and 3 / 4 respectively. Find the circumference of the triangle
A book, the first day read a quarter of the book, the second day read the remaining two-thirds, there are 60 pages not read, how many pages of this story book?
Spend 95 yuan to buy two kinds of notebook A and B, a bought 100, has bought 30, a is a third of B, a and B notebook unit price each how many yuan?
He walked 295 kilometers on foot, 7 days on the level road and 8 days on the mountain road. It was 10 kilometers faster on the level road than on the mountain road every day. During this period, how many kilometers did he walk on the mountain road and the peace road every day?

1. Triangle circumference = 3 / 5 + 2 / 3 + 3 / 4 = (36 + 40 + 45) / 60 = 121 / 60 = 2 and 1 / 60
2. 60 / {[1-1 / 4 - (1-1 / 4) (2 / 3)]} = 60 / {3 / 4-2 / 4} = 60 / {1 / 4} = 240 (page)
3、100x+30y=95
x=y/3
100x + 30 * 3x = 95, x = 95 / 190 = 0.5 (yuan); y = 1.5 (yuan)
The unit price of notebook a is 0.5 yuan, and that of notebook B is 1.5 yuan
4、7(a+10)+8a=295
15A = 225, a = 15 (km)
Take Pinglu 7 (a + 10) = 175 km; take Shanlu 8A = 120 km
Walk 25 kilometers on the level road and 15 kilometers on the mountain road every day