Question

the length of a rectangle is 7mm longer than its width. its perimeter is more than 62mm. let w equal the width of the rectangle.

A. write an expression for the length in terms of the width.

B. use these expressions to write an inequality based on the given information.

C. solve the inequality, clearly indicating the width of the rectangle.

Answer 1

please help me:)

Answer 2

The length is 7 longer than the width.
\[\large L=7+W\]Understand how I did part A?
Look for keywords in the sentence. IS means equals. LONGER THAN let us know we had to add 7 to the width.

Answer 3

The perimeter is MORE THAN 62mm.\[\large P \gt 62\]Since it's a rectangle we want to recall the formula for Perimeter.\[\large P=2L+2W\]
Substituting this in gives us,\[\large \color{ #CC0033}P \gt 62 \qquad \rightarrow \qquad \color{ #CC0033}{2L+2W} \gt 62\]

Answer 4

To solve the inequality, we'll have to make another substitution using the Length/Width relationship we found at the start.\[\large L=7+W\]Plugging this in gives us,\[\large 2\color{#3366CF}L+2W \gt 62 \qquad \rightarrow \qquad 2(\color{#3366CF}{7+W})+2W \gt62\]

Answer 5

Now we have an inequality that only involves W, not L.
So we can solve for W from here.

Answer 6

Confused by any of that? :O

Answer 7

no im starting to understand

Answer 8

To finish solving for W, we'll first DISTRIBUTE the 2 to each term inside the brackets.\[\large 2(7+W)+2W \gt 62 \qquad \rightarrow \qquad 14+2W+2W \gt 62\]We'll subtract 14 from each side,\[\large 2W+2W \gt 48\]We'll combine like terms,\[\large 4W \gt 48\]Dividing both sides by 4 gives us our final answer,\[\large W \gt \frac{48}{4} \qquad \rightarrow \qquad W \gt 12\]

Answer 9

For this particular rectangle, the width has to be at least 12mm.

I think those are all the steps you will need.
Take a look at them and try to understand what's going on.

Ask questions if you're confused by any particular part.

Answer 10

how do you get 12mm

Answer 11

There are a bunch of algebra steps listed to solve for W, you will eventually get a solution of \(W \gt12\). The Width (W) is greater than 12(mm).

Answer 12

okay thank you soo much:D