Question

The length of a rectangle is x times the square root of 100. The width is one-half y more than three-halves x. Given that the area of the rectangle is 125 cm2, which equation could represent the rectangle in terms of x and y?

Answer 1

5xy + 15x2 = 125

Explanation:

5xy + 15x2 = 125

L = (x

100

)

W = (

1

2

y −

3

2

x)

(x

100

)(

1

2

y +

3

2

x) = 125

(10x)(

1

2

y +

3

2

x) = 125

5xy + 15x2 = 125

Answer 2

`3x^2+xy-25=0`

Explanation:

The length of the rectangle is:

`L=x\cdot √(100)=x\cdot 10=10 x`

The width of the rectangle is:

`W=(1)/(2)y+(3)/(2)x`

The area of the rectangle, which is the product between length and width, is equal to 125 cm^2:

`A=L\cdot W=125`

Substituting the expressions for L and W found before, we get:

`(10x)((1)/(2)y+(3)/(2)x)=125\\(10x)(y+3x)=250\\10xy+30x^2=250\\3x^2+xy-25=0`