Question

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?

Answer 1

10m ;

500 m²;

300 m²

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