Problem Solving

A rectangular tabletop consists of a piece of laminated wood bordered by a thin metal strip along its four edges. The surface area of the tabletop is x square feet, and the total length of the strip before it was attached was x feet. If the tabletop is 3 feet wide, what is its approximate length, in feet?

a) 12
b) 10
c) 9
d) 8
e) 6

OA: E

Let a be the length of the table.

Length of strip: 3 + a + 3 + a = x
6 + 2a = x

Surface area: 3a = x

Equate the x's:

3a = 2a + 6
a = 6

Answer E

Thank you very much, Moutar!

why do u equate perimeter to area?

how do u know that perimeter = area of rectangle?

thanks in advance

You have a rectangular wooden piece bordered by metal strip (rectangle). From the question total length of the strip = x = Perimeter of the metal strip.

We also know that the width of the strip = 3 (i.e the width of the table top) hence x= 3+a+3+a = 6+2a where a = length of table top(metal strip).

Also given is SA of table top =x = 3*a now solving
x= 6+2a,
which implies 3a=6+2a hence a = 6 E.)

- Deepak