One side of a rectangle is 2 yd longer than two times another side. The area of the rectangle is 84 yd2. Find the length of the shorter side.

6 yds

Step-by-step explanation:

If we label the shorter side as x, the longer side can be represented as 2x + 2. Now, we can write an equation to model the situation. The area of a rectangle is the sides multiplied by each other:

84 = x(2x + 2)

84 = 2x^2 + 2x

Since all terms are divisible by two, we can divide both sides by it:

42 = x^2 + x

We can write the quadratic equation in standard form:

x^2 + x - 42 = 0

Now, we can factor. We are looking for numbers that multiply to -42 and add to 1. These numbers are 7 and -6. Factored the equation would be written as followed:

(x + 7)(x - 6) = 0

Using the zero-product property, we can obtain two equations and solve them:

x + 7 = 0

x  = -7

x - 6 = 0

x = 6

Since the side of a rectangle can't be negative, the answer must be 6 yds.

i think it is everything has to equal 180 so, if i correct 4=c. 6=d. 8=a. 7=b. and the last question would be c. because they are parallel lines and they are congruent.

step-by-step explanation:

the reason everything has to equal to 180 is because that is how it works. i'm guessing that is its rule. 4 and 8 are congruent and parallel so, that would be 30+30 because they have the same number. it would equal 60. 6 and 7 are congruent and parallel so, that would be 30+30 because they have the same number. it would equal 60. 60+60 is 180. so, now you have your answer

answer: bearing in mind that a rectangle has a perimeter of length + length + width + width.

step-by-step explanation:

p = perimeter

l = length

x=width

p = 2l + 2x

p = 2(l+x)     < ==== perimeter of the base of the box.