ALGEBRA QUESTIONS?? Check details please and thank you...?

Question

1.) The formula for the surface area of a rectangular prism is A+ 2(lw +hl + wh). Solve the formula for w.

2.) The length of a rectangle is 3cm greaterthan its width. The perimeter is 24 cm. Find the dimensions of the rectangle.

Answer 1

Let w = width

w + 3 = length

2w + 2(w+3) = 24

2w +2w + 6 = 24

        4w + 6 = 24

               4w = 18

                 w = 4.5

Length = w +3 = 4.5 + 3= 7.5

Let w= the width of the rectangle. Thus, the length equals w + 3, if it is 3 greater than the width.

If we know that the perimeter is 24, that means all 4 sides of the rectangle add up to 24, of which parallel sides have the same dimension. Thus, you form the equation 2w + 2(w + 3) = 24, solve it, and get that the width is 4.5 cm and the length is 7.5 cm.  

Answer 2

1.)

A=2(lw+hl+wh)

A=2lw+2hl+2wh

A=2lw+2wh+2hl

A=w(2l+2h)+2hl

A / 2(l+h+hl) = w

2.)

Perimeter=2l+2w

24=2(l+w)

12=l+w

l=w+3

12=w+(w+3)

12=2w+3

9=2w

4.5=w

Verify

w=4.5, so l=7.7

P=2l+2w

P=2(4.5)+2(7.5)

P=9+15

P=24

Our answer is correct:

l=7.5 and w=4.5 cm