Saritha will construct a rectangle that has a height of 4 units and an area of up to 48 square units. What inequality represents all the possible length in units of bases, b, that Saritha can use to reconstruct the rectangle ?

Remember that for a square of height H and length L, the area will be:

A = H*L

In this case, we know that the height is H = 4 units.

And the area is up to 48 square units

This means that the maximum possible area of this rectangle is 48 square units.

Then we have:

A ≤ 48 square units.

And we also could add:

0 square units < A ≤ 48 square units.

Now we can replace A by H*L = L*(4units)

0 square units < L*(4 units) ≤ 48 square units.

Now we need to divide all 3 sides by 4 units.

(0 square units)/(4 units) < L  ≤ (48 square units)/(4 units)

0 units < L  ≤ 12 units.

This is the range of lengths that Saritha can use to reconstruct the rectangle.

Now if we define b as the length of the bases, then we will use:

b =  height = 4units.

Then:

1b = 4units.

(1 b/4units) = 1

This means that:

12 units = (12 units)*1 = (12 units)*(1 b/4units) =  (12/4) b = 3 b

Then the range of possible values of L is:

0b < L  ≤ 3b

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