The length of a rectangle is 5yd longer than its width. If the perimeter of the rectangle is 54yd , find its length and width.

L = w + 5

P = 2(L+w) = 42

L + w = 21

w+5 + w = 21

2w + 5 = 21

2w = 16

w = 8 ft

L = w+5 = 13 ft.

Rectangle is 13 ft by 8 ft

Area = 13(8) = 104 ft2

Check: P = 2(L+w) = 2(13+8) = 2(21) = 42 ft

Explenation

L=16*2=32

W=11*2=22

P=32+22=54

P=54

the length is 5yd longer than its width

16-11=5

step-by-step explanation:

equation

you are asked to write the equation

  expression = 0

using the given expression. when you do that, you have

  2x^2-2x-12 = 0

factoring

you can see that each of the coefficients is even, so a factor of 2 can be removed immediately.

  2(x^2 -x -6) = 0

if you multiply the binomials (x+a)(x+b), you get

  (x +a)(x +b) = x^2 +(a+b)x +ab

this tells you the coefficient of x is the sum of two factors of the constant term. here, that means -1 is the sum of two factors of -6. we want to know those factors so we can factor the trinomial.

  -6 = -1×6 = -2×3 = -3×2 = -6×1

the factor pair that sums to -1 is {-3, 2}, so our factorization is

  2(x -3)(x +2) = 0

solutions

the solutions to this equation are the values of x that make the product zero. a product is zero only when only of the factors of the product is zero. here, that means

  x - 3 = 0

  x = 3 . . . add 3 to both sides of the equation

or

  x +2 = 0

  x = -2 . . . add -2 to both sides of the equation

the solutions to the equation are x=3 or x=-2. both of these values of x satisfy the equation—they make it be true.

step-by-step explanation: