Question

The rectangle shown has a perimeter of 78 cm and the given area. Its length is 3 more than five times its width. Write and solve a system of equations to find the dimensions of the rectangle.

Answer 1

To find the dimensions of the rectangle with the given perimeter of 78 cm and the relationship between length and width, a system of equations is established and solved to determine the width and length.

Step-by-step explanation:

To find the dimensions of a rectangle given its perimeter and area, with the length being a function of the width, we set up a system of equations. Let width be represented by w and length by l. The problem states that the length is three more than five times its width, so we have l = 5w + 3. The perimeter of a rectangle is given by the formula P = 2l + 2w, and we know the perimeter is 78 cm, leading to the equation 2(5w + 3) + 2w = 78. Solving this, we find the width, and substituting back, we get the length.

Answer 2

So W is going to stand for width and L is going to stand for length.

L= 2W+6

78=2L + 2W

Those are the two equations you will use. So plug in L=2W+6 into the other one and solve.

78= 4W+12 +2W

(simplify)

78=6W+12

(-12 from both sides)

66=6W

(divide by 11)

W=11

Replug W into your equation to find L.

L=22+6

(simplify)

L=28

I hope this is right

Step-by-step explanation: