Answered

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The perimeter of a rectangle is 20 inches and it’s area is 24 square inches. What are its dimensions?

Sagot :

Solution

For this case we know that:

P= 20 in represents the perimeter

A= 24 in^2 represent the area

We also know that by definition:

P= 2W+ 2H

A= W*h

Where W= width and H= height

So we have this:

20 = 2(W+H) (1)

24= WH (2)

Solving W from the (2) equation we got:

W= 24/H

Replacing into the first equation we got:

20 = 2 (W+H)

10= W+H= 24/H + H

10 = (24+H^2)/H

10H= 24 +H^2

H^2 -10H +24=0

(H-6)(H-4)=0

Then H= 4in or H=6in

Solving for W we got:

W= 24/4 = 6in, W= 24/6=4in

Then the dimensions are:

6 in and 4 in

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