Question

The rectangle shown has a perimeter of 58 cm and the given area. Its length is 4 more than four times its width. The area of the rectangle is 120 cm2. Write and solve a system of equations to find the dimensions of the rectangle.

Answer 1

The length of the rectangle is 24cm and the width of the rectangle is 5cm.

Explanation:

Length=4+4w

Perimeter=L+W+L+W

P=4+4w+w+4+4w+w

P=10w+8

Now that we have our equation we can solve it. Since the perimeter is 58cm, you can switch the letter P for 58.

58=10w+8

Then subtact 8 from both sides.

50=10w

Then divide both sides by 10.

5=w

Now we know that the width is 5cm, but we still have to solve for length.

L=4+4w

Trade the w for 5 because the width is 5cm.

L=4+4x5

L=4+20

L=24

The length is 24cm.

Answer 2

Answer: w=5

Explanation:

58=l+l+w+w

l=4w+4

58=(4w+4)+(4x+4)+w+w

58=8w+8+w+w

58=10w+8

50=10w

5=w

w=5

l=4w+4

l=4(5)+4

l=20+4

l=24

check:

w=5, l=24,

5*24=120

our answer is correct