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The width of a rectangle is 6 cm less than its length. If its perimeter is 80 cm then its lengths (in cm) and area (in cm²) are respectively

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Start by stating the given info as mathematical expressions:

1. "The width of a rectangle is 6 cm less than its length."

w=l-6

2. "Its perimeter is 80 cm."

P=80

Using the formula for perimeter (
P=2l+2w) we can show:

80=2l+2w.

We now have 2 equations in 2 unknowns and can solve by substitution:

80=2l+2w

80=2l+2(l-6)

80=2l+2l-12)

92=4l

l=23

The length is 23cm.

Having the length w can then find the width:

w=l-6

w=23-6

w=17

The width is 17cm.

And finally the area:

A=lw

A=(23)(17)

A=391

The area is
391cm^(2).


As a check we can use the known perimeter:

80=2l+2w

80=2(23)+2(17)

80=46+34

80=80 Checks true.
User Shoaib Ijaz
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