Set up an algebraic equation and then solve the following problem. the width of a rectangle is 7 feet less than its length. if the area of the rectangle is 170 square feet, then find the length and width.

Let x be the width and let y be the length. To find the area, the formula is W*L.

The width is 7 less than the length: x = y-7

We only want one variable to deal with first, so we could also write:

y = x+7

Then we have,

x*(x+7) = 170

x²+7x-170 = 0

(x+17)(x-10) = 0

So x = -17, 10

When x = -17, y = -17+7 = -10

When x = 10, y = 10+7 = 17

But we cannot have negatives so the first solution does not work.

The width is 10 and the length is 17.

∠1≅∠2 by the alternate exterior angles theorem.

step-by-step explanation:

given, a ∥ b and ∠1 ≅ ∠3 .we have to prove that e ∥ f

we know that ∠1≅∠3 and that a || b because they are given. we see that by the alternate exterior angles theorem. therefore, ∠2≅∠3 by the transitive property. so, we can conclude that e || f by the converse alternate exterior angles theorem.

we have to fill the missing statement.

transitivity property states that if a = b and b = c, then a = c.

now, given ∠1≅∠3 and by transitivity property ∠2≅∠3 .

hence, to apply transitivity property one angle must be common which is not in result after applying this property which is ∠1.

the only options in which ∠1 is present are ∠1 and ∠2, ∠1 and ∠4

∠1 and ∠4 is not possible ∵ after applying transitivity we didn't get ∠4.

hence, the missing statement is ∠1≅∠2.

so, ∠1≅∠2 by the alternate exterior angles theorem.

step-by-step explanation: