Question

The perimeter of a rectangle is 80x. The base is two times the height. In terms of x, what are the dimensions of the rectangle?

a.
h = 10x; b = 10x
c.
h = 10.3x, b = 20.6x
b.
h = 13.3x; b = 26.6x
d.
h = 5x; b = 25x

Answer 1

Answer:
h = 13.3x; b = 26.6x

Step-by-step explanation:
Perimeter of the rectangle = 2(base+height)
80x = 2(base+height)
base + height = 40x ........> I

Now, we are given that the base is 2 times the height, this means that:
base = 2*height ..........> II

Substitute with II in I:
base + height = 40x
2*height + height = 40x
3*height = 40x
height = 13.3x

Substitute with the height in equation II to get the base as follows:
base = 2*height
base = 2 * 13.3x = 26.6x

Hope this helps :)

Answer 2

By definition we have that the perimeter of a rectangle is given by:
P = 2b + 2h
Where,
b: base
h: height
Also, as a data of the problem we have:
base is two times the height:
b = 2h
Substituting we have:
P = 2 (2h) + 2h
Clearing h:
6h = P
h = P / 6
h = (80x) / 6
h = (40/3) x
The base will be
b = 2h
b = (80/3) x
Answer:
the dimensions of the rectangle are
b = (80/3) x
h = (40/3) x
b. h = 13.3x; b = 26.6x