Seventh grade math exercises 1. In △ ABC, ab = 15, BC = 14, AC = 13, find s △ ABC

Seventh grade math exercises 1. In △ ABC, ab = 15, BC = 14, AC = 13, find s △ ABC

Using Helen's formula:
Helen's formula, also translated into Hiram's formula and Hailong's formula, is said to be the formula discovered by Hiram II, king of Syracuse in ancient times, who used the three sides of a triangle to calculate the area of the triangle. However, according to Morris Kline's book published in 1908, this formula was actually discovered by Archimedes and published in the name of torhiram II
Suppose there is a triangle with side lengths of a, B and C respectively. The area s of the triangle can be obtained by the following formula: S = under the root sign (P (P-A) (P-B) (P-C))
And P: (a + B + C) / 2 in the formula
Because any n-sided polygon can be divided into n-2 triangles, Helen's formula can be used to calculate the area of the polygon. For example, when measuring the area of the land, you don't need to measure the height of the triangle, just need to measure the distance between two points, you can easily derive the answer

2 and one third minus five fourths minus nine fourths?

=7 out of 3 minus 5 out of 14 minus 9 out of 14
=7 out of 3 minus (5 out of 14 plus 9 out of 14)
=7 out of 3 minus 3 out of 3
=4 / 3

Xiaoming's tree is half of Xiaogang's and Xiaodong's, and Xiaogang's is one third of Xiaoming's and Xiaodong's. it is known that Xiaodong has 10 trees
How many trees can we plant?

x=1/2y+5
y=1/3x+10/3
x=8 y=6
Xiaoming 8, Xiaogang 6

The sum of a natural number and its reciprocal is 5.2
Today is the end of the day

Let the natural number be X
Then: x + 1 / x = 5.2
There are 5x ^ 2-26x + 5 = 0
(5x-1)(x-5)=0
The solution is x = 5 or x = 1 / 5
So the natural number is 5

Three five, one and one, miscellaneous calculation can make the result equal to twenty-four,

5*(5-1/5)

Make a 5 cm deep uncovered cuboid box with a 40 cm long and 20 cm wide rectangular sheet iron. Find the maximum volume of the uncovered cuboid box

After cutting the small square with side length of 5cm from the four corners, it can be made
Length = 40-5-5 = 30 width = 20-5-5 = 10 height = 5
Volume = 30 × 10 × 5 = 1500 cc

There are 56 woodworking factories. Two workers can process three tables a day, and three workers can process 10 chairs a day. Now how can we arrange the labor force to make the living environment better
There are 56 workers in the woodworking factory. Two workers can process three tables a day, and three workers can process 10 chairs a day. Now how to arrange the labor force to make one table and four chairs match? Two yuan per time

Arrange x people to process the table and y people to process the chair
X+Y=56
4×3/2 X=10/3 Y
The solution is: x = 20, y = 36
Answer:

24 points=______ Time & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; 6600 kg=______ T 0.8 ha=______ Square meters & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; 3.2 cubic decimeters=______ Ml

(1) 24 points = 0.4; (2) 6600 kg = 6.6 tons; (3) 0.8 hectare = 8000 square meters; (4) 3.2 cubic decimeter = 3200 ml; so the answer is: 0.4, 6.680003200

New year's calendar is 15 yuan per book. How much does it cost to buy 10 new year's calendars?

It costs only four to buy five. 15 × 4 = 60
Ten copies are two five copies, and the cost is 60 × (10 △ 5) = 60 × 2 = 120 yuan
——————————————————————————————————————————- form a formula (15 × 4) × (10 △ 5) = 60 × 2 = 120

Simplification: (1) (√ 12 + √ 27) / √ 3
Simplification:
（1） （√12+√27）/√3
（2） （√3+√2)(√3-√2)

It is proposed that square (2 √ 3 + 3 √ 3) / √ 3 = 5 √ 3 / √ 3 = 5
Using the complete square difference formula, the original formula = (√ 3) ^ 2 - (√ 2) ^ 2 = 3-2 = 1