the lngth and width of a rectangle can b expressed as (3x + 1) and (2x - 7). write an expression for the perimeter and an expression for the area

Answer 1

First you need your formulas for perimeter and for area of a rectangle.

perimeter is the distance around it, which is p=2l+2w

This means you multiply the length times 2 and the width times 2 and then add them (in this case, combine like terms).

Step 1: 2(3x+1)+2(2x-7)

Step 2 (distribute): 2*3x+2*1 + 2*2x + 2*-7

6x + 2 + 4x -14

Step 3 (combine like terms):

6x + 4x=10x 2 - 14= -12

Perimeter expression: 10x - 12

Area of a rectangle is l*w This means you multiply the length times the width

Step 1: (3x+1) * (2x-7)

Step 2: FOIL First term times first term: 3x*2x=6x^2

Outer term times outer term: 3x*-7= -21x

Inner term times Inner term: 1*2x= 2x

Last term times last term: 1*-7= -7

Step 3: Combine like terms: -21x +2x= -19x

Step 4: Create polynomial with simplified terms for area expression: 6x^2 - 19x -7