Draw a triangle with an area of 12 cm2 and a base-height ratio of 3∶2.
The analysis base is 6 cm and the height is 4 cm.
2. Draw a rectangle with a perimeter of 12cm and an aspect ratio of 2∶ 1.
Analysis of 12÷2=6 (cm)
So the width is 6÷(2+ 1)=2 (cm).
Length: 2× 2 = 4cm
Second, solve practical problems.
1. This shop has delivered a batch of color TV sets. The ratio of the number of units sold to the number of remaining units is 7∶3, which shows that the number of units sold is more than the number of remaining units 12. How many color TVs are there in this batch?
Solution 12(7-3)= 3 (Taiwan Province)
3×(7+3)=30 (unit)
2. The TV factory produced 6000 TV sets in the first quarter, and produced more 1 set in the second quarter than in the first quarter. How many TV sets were produced in the second quarter?
Solution 6000× (1+1in8) = 6000× 9in8 = 6750 (unit)
3. In the school "Sports Meeting" skipping competition, Liu Hong jumped 160 times, Li Ming jumped 4/5 times as much as Liu Hong, and Zhang Hua jumped 7/8 times as much as Li Ming. How many times did Zhang Hua jump?
How many times does Li Ming jump?
160× 4/5 = 128 (below)
How many times does Zhang Hua jump?
128× 7/8 =112 (below)
4. Make a rectangular glass goldfish bowl with no cover, 80 cm long, 60 cm wide and 40 cm high.
(1) How many square meters of glass does it take to make this goldfish bowl?
(2) If the height of water is 4/5 of the height of the goldfish bowl when raising fish, how many liters of water are there in the goldfish bowl?
(3) For the sake of beauty, put 9.6 cubic decimeters of stones in the goldfish bowl. How many centimeters will the water surface rise at this time?
Solution (1) 80× 60+2× (80× 40+60× 40) = 4800+2× 5600 =16000 (square centimeter).
16000m2 =1.6m2.
Therefore, it takes at least 2.08 square meters of glass to make this goldfish bowl.
(2)80×60×40×5 = 153600 (cubic centimeter)
153600 cubic centimeters = 153.6 liters
(3)9.6 cubic decimeter =9600 cubic centimeters
9600(80×60)= 2 cm
The school bought eight footballs and four basketballs, and one went to 360 yuan. The price of basketball is four times that of football. What is the price of a football?
Suppose the price of a football is X yuan, then basketball is 4x yuan.
8x+4 4x=360
24x=360
Solution, x= 15
6. The following is an expanded view of a cuboid (unit: cm). Find the surface area and volume of a closed cuboid
The lengths of the three sides are 12, 9 and 6 cm respectively.
Therefore, the surface area is 2× (12× 9+12× 6+9× 6) = 468 (square centimeter).
Volume: 12×9×6=648 (cubic centimeter)
7. Fill 105 liters of water into two containers A and B, which can be filled with 1 of two containers A and B, or 1 of two containers B and A. What is the capacity of each container? (Equation solving)
If the capacity of container B is x liters, then A = 105-2+0 x.
x+ 1( 105-2 1x)= 105。
Multiply both sides of the equation by 6 at the same time.
6x+2 10-x=630
5x=420
x=84
A: 105-2: 1.84 = 63 (liter)
8. There is a rectangular lawn with a length of 20m and a width of12m. The gardener wants to trim it into the largest square lawn. How much less is the square lawn than before?
The original solution area is
20× 12=240 (square meter)
Later, the area was
12× 12= 144 (m2)
Missing: 240- 144=96 (m2)
Reduction: 96 ÷ 240×100% = 0.4×100% = 40%.