Junior 3 Mathematics Junior 3 Mathematics Please answer in detail, thank you 30 20 38 16

Because 30 degrees can be a top angle or two equal corners.

For example: 30 degrees, 30 degrees, 120 degrees.

30 degrees, 75 degrees, 75 degrees.

All have an isosceles triangle with an angle of 30 degrees, absolutely not similar!

A 60-degree triangle must be an equilateral triangle, and it must be similar!

90 degrees and 120 degrees can only be used as top angles, so it must be similar!!

A is wrong.

b, if there is an angle of 60, if it is a top angle, then the two bottom angles are 60, if it is a bottom angle, then the top angle is 60, so it is an equilateral triangle, so it is similar.

c. There is an angle of 90, which must be the top angle, otherwise the inner angle is greater than 180, the top angle is 90, and the bottom angle is 45, so it is similar.

d, there is an angle of 120, that must be the top angle, so it is similar.

c. If the low angle is 90°, that's wrong, you see if it's correct.

Choose AA---1... 30 degrees, 30 degrees, 120 degrees 2... 30 degrees, 75 degrees, 75 degrees.

b--- 60 degrees, 60 degrees, 60 degrees.

c--- 90 degrees, 45 degrees, 45 degrees.

d--- 120 degrees, 30 degrees, 30 degrees.

Choose A, the 30° angle can be the top angle or the bottom angle. The triangles are not the same.

One is 30 ° 30 ° 120 ° and the other is 30 ° 75 ° 75 ° not similar.

Solution: (1) Because the sum of the lengths of the two diagonals of the diamond is exactly 60cm, and one of them is x, the length of the other diagonal can be obtained as 60-x

And because the diagonal lines of the diamond are bisected perpendicular to each other.

Therefore, the area of the rhombus is s=4 (1 2) (x 2) [60-x) 2]=1 2(60x-x 2).

2)s=1/2(60x-x^2)=-1/2(x^2-60x+900-900)=-1/2(x-30)^2+450

Therefore, when x=30cm, the diamond-shaped kite has the largest area s, which is 450.

1、s=（1/2）x(60-x)=-(1/2)x^2+30x

2. The formula will not be used for formula: when x=-(b 2a), the maximum value of s: (4ac-b 2) 4a

s = 60x-x2 (squared) = - (x2-60x+30*30-30*30) = - (x-30)(x-30)+900

So when x=30, the area s is up to 900

Use the root finding formula to make the expression, and the part under the root number is as follows:

a-1）^2-（2b+a）^2

If there is a non-negative number under the root number, then the equation has a real root.

Therefore a=1 b=

Its roots are two equal solid roots.

x=-2

The diagonals of the diamond are bisected perpendicular to each other.

Let the diagonal lines be 3a and 4a long, respectively

It is derived from the Pythagorean theorem.

The side length of the diamond is (3a 2) +4a 2) = the perimeter of the diamond is .

then a = 23a = 6 and 4a = 8

The area of the diamond is half of the product of the diagonal, i.e., 3a 4a 2 = 6 8 2 24 square centimeters.

The diagonal lines are 6xcm and 8xcm long, respectively

Because the circumference is 20cm, the side length is 5cm

3x)²+4x)²=5²

The solution yields x1 = 1 and x2 = -1 (round).

So 6x = 6, 8x = 8

That is, the diagonal lines are 6cm and 8cm long, respectively

s=6×8/2=24cm²

The side length is 5 centimeters, the diagonal is 6 centimeters, the one is 8 centimeters, and the area is 24 square centimeters.

Because the diamond shape has four equal sides.

So the length of each side is: 20 divided by 4=5.

And because his diagonals are bisected perpendicular to each other, he consists of four right triangles, and if one diagonal is 3x, then the other is 4x

From the Pythagorean theorem, the square of 5 = the square of 3x + the square of 4x is solved to get x=1 or x=-1 (not in question, rounded) Because the resulting number is half of the two diagonals, the diagonal lengths are 6 and 9, respectively, and the area is equal to half of the product of the two diagonals: (6x8) divided by 2 = 24