Rectangle area 48, length 8, find the width Easy

The question

Question: find the width w of a rectangle with area 48 square units and length 8.

1 Write the rule

The area of a rectangle is length times width.

So A = length × width.

2 Put the numbers in

The area is 48 and the length is 8.

So 8 × w = 48.

Careful!

The area is times, not plus.

So we divide by 8.

We do not take it away.

3 Remove the × 8

We want w by itself.

The times 8 is in the way.

To remove times 8, we divide by 8.

We do it on both sides.

Why both sides?

The = sign means both sides are the same amount.

If we change only one side, they are not the same any more.

8 divided by 8 is 1.

So just w is left.

48 divided by 8 is 6.

So the width is 6.

4 Check

Let's check: length times width, 8 times 6.

We get 48, the area.

So the width is right!

Let's look back.

First: write the rule.

Then: put the numbers in.

Then: remove the × 8.

Last: check.

▶ Watch it solved

Rectangle perimeter 30, length 9, find the width Medium

The question

Question: find the width w of a rectangle with perimeter 30 and length 9.

1 Write the rule

The perimeter is the way all around the edge.

We add every side.

Walk around: length, width, length, width.

P = l + w + l + w.

2 Put the numbers in

The perimeter is 30 and the length is 9.

So 9 + w + 9 + w = 30.

Careful!

The length is there twice, and the width is there twice too.

3 Group like terms

The plain numbers go together: 9 plus 9 is 18.

The w's go together: two of them, 2 times w.

Now we have 18 + 2 × w = 30.

4 Remove the 18

We want 2 × w by itself.

The 18 is in the way.

To remove 18, we take away 18.

We do it on both sides.

Why both sides?

The = sign means both sides are the same amount.

If we change only one side, they are not the same any more.

18 and − 18 make zero.

Cross them out.

30 minus 18 is 12.

5 Remove the × 2

To remove times 2, we divide by 2.

We do it on both sides, so they stay equal.

2 divided by 2 is 1.

So just w is left.

12 divided by 2 is 6.

So the width is 6.

6 Check

Let's check: walk around and add.

We get 30, the perimeter.

So the width is right!

Let's look back.

First: write the rule.

Then: put the numbers in.

Then: group like terms.

Then: remove the 18.

Then: remove the × 2.

Last: check.

▶ Watch it solved

Circle area 50.24, find the radius Harder

The question

Question: find the radius r of a circle with area 50.24 square units.

1 Write the rule

The area of a circle is π times the radius squared: A = π × r².

π is a special number for circles.

It is about 3.14.

Now put the numbers in: A = 50.24 and 3.14 for π.

Careful!

50.24 divided by 3.14 is r², the radius times itself.

We still need its square root.

2 Remove the × 3.14

We want r² by itself.

The times 3.14 is in the way.

To remove times 3.14, we divide by 3.14.

We do it on both sides.

Why both sides?

The = sign means both sides are the same amount.

If we change only one side, they are not the same any more.

3.14 divided by 3.14 is 1.

So just r² is left.

Check the division: 3.14 times 16 is 50.24.

50.24 divided by 3.14 is 16.

So r² = 16.

3 Take the square root

r times r is 16.

So r is the square root of 16.

The square root of 16 is the positive number that times itself makes 16.

4 times 4 is 16.

So the radius is 4.

4 Check

Let's check: put r = 4 back in the rule.

We get 50.24 again.

So the radius is right!

Let's look back.

First: write the rule.

Then: remove the × 3.14.

Then: take the square root.

Last: check.

▶ Watch it solved