Cynthia besch wants to buy a rug for a room that is 20 ft wide and 31 ft long. she wants to leave a uniform strip of floor around the rug. she can afford to buy 350 square feet of carpeting. what dimensions should the rug have?

The dimensions should the rug have: length = 25 feet and width of 14 feet.

Step-by-step explanation:

Dimension of the room is 20 ft wide and 31 ft long

Area of rug purchased by Cynthia Besch =

Suppose she leave strip of floor which is x ft thick.

Length of the rug= l = (31-x) ft

Width of the rug= w = (20-x) ft

Area of the rug,A = l × w

x = 45 , 6

x = 6 (accept), x= 45 ,(reject, larger than length of the room )

Length of the rug= l = (31-x) ft = 31 - 6 ft = 25 ft

Width of the rug= w = (20-x) ft = 20 - 6 ft = 14 ft

answer: 204

step-by-step explanation:

we are told that the revenue is

x⋅(4080−10x)=−10x^2+4080x

this is a quadratic function, so to maximize it we should find the x-value of its vertex. recall that the x-value of the vertex of the parabola ax^2+bx+c is given by the formula −b/2a.

so in this case, we have a=−10 and b=4080, so the x-value of the vertex is

−b/2a= −(4080)/2(−10)=204