Question

A rectangular-shaped dining room table is modeled by the figure given below. A) Write an equation to represent the area of the dining room table. B) If the the area of the table is 112 ft2, what are the dimensions of the dining room table?

Answer 1

A) (x+10)(x+4) = ?

B) (x+10)(x+4) = 112, solve for x

Step-by-step explanation: you multiply the two equations to get the area.

Answer 2

a)
`(x^(2) +14x+40)ft^(2)`

b)14ft, 8ft

Explanation:

a) Area of Rectangle = Length x Breadth

=
`(x+10)(x+4)\\=x^(2) +4x+10x+40\\=(x^(2) +14x+40) ft^(2)`

b) Given Area of rectangle =
`112ft^(2)`

`x^(2) +14x+40=112\\x^(2) +14x-72=0 (Quadratic Equation)\\\\`

Quadratic Equations:
`ax^(2) +bx+c = 0\\`

In this case, a = 1, b = 14, c = -72

`\frac{-b+/-\sqrt{b^(2)-4ac } }{2a} \\= \frac{-14+/-\sqrt{14^(2) 4(1)(-72)} }{2(1)} \\= 4 or - 18 (reject)`

We reject negative values.

so x = 4,

The length of table = (x+10) ft = 4+10 = 14ft

The breadth of the table = (x+4) ft = 4 + 4 = 8ft