Question

Given that a rectangle has a length of 5 2 x + 10 with a width of 5 2 x + 5, which expression represents the area of the rectangle? A) 25x2 2 + 75x 2 + 50 B) 25x2 4 + 75x 4 + 50 C) 25x2 4 + 75x 2 + 50 D) 25x2 2 + 75x 4 + 50

Answer 1

C

Explanation:

Apply FOIL method (First, Outer, Inner, Last) to multiply the length and width binomial expressions.

Answer 2

Option c is correct

`(25)/(4)x^2+(75)/(2)x+50`

Explanation:

Area of the rectangle (A) is given by:

`A= lw` ....[1]

where,

l is the length and w is the width of the rectangle.

As per the statement:

Given that a rectangle has a length of
`(5)/(2)x+10` with a width of
`(5)/(2)x+5`

⇒l =
`(5)/(2)x+10`

and w =
`(5)/(2)x+5`

Substitute in [1] we have;

`A = ((5)/(2)x+10) \cdot ((5)/(2)x+5)`

⇒
`A = (25)/(4)x^2+(25)/(2)x+(50)/(2)x+50`

Combine like terms we have;

`A = (25)/(4)x^2+(75)/(2)x+50`

therefore, the expression represents the area of the rectangle is,
`(25)/(4)x^2+(75)/(2)x+50`