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19.01.2021 •
Mathematics
The aspect ratio of a rectangle is (length/width). Yolanda and Zhang each have a garden in the shape of a rectangle that is surrounded by 120 meters of fence. Yolanda's rectangle has aspect ratio 2 and Zhang's rectangle has aspect ratio 5.
A) Width of Zhang's garden =.
B) Area of Zhang's garden =.
C) How many square meters larger is the area of Yolanda's garden than Zhang's garden?
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Ответ:
10m ;
500 m²;
300 m²
Step-by-step explanation:
Aspect ratio = Length / width
Perimeter = 120
Perimeter, P = 2(l + b)
l = Length, b = width
Yolanda :
Aspect ratio = 2
l/b = 2
l = 2b
Hence,
120 = 2(2b + b)
120 = 2(3b)
120 = 6b
b = 120/6
b = 20
Zhang :
Aspect ratio = 5
l/b = 5
l = 5b
Hence,
120 = 2(5b + b)
120 = 2(6b)
120 = 12b
b = 120/12
b = 10
Area of Zhang :
Length * width
5b * b
5(10) * 10
50 * 10
= 500m²
Area of Yolanda :
Length * width
2b * b
2(20) * 20
40 * 20
= 800 m²
Difference :
800m² - 500m²
= 300m²
Ответ: