Question

The perimeter of a rectangle is 56 inches. The ratio of the length to the width is 6:1. Find the length and width.

Answer 1

The rectangle has a length of 24 inches and a width of 4 inches, discovered by solving a set of equations derived from the given perimeter and length to width ratio.

Step-by-step explanation:

To solve for the length and width of the rectangle, knowing the perimeter is 56 inches and the length to width ratio is 6:1, we must first set up two equations based on the information given:

• 2(length + width) = Perimeter
• Length to width ratio = Length/Width

From the length to width ratio of 6:1, we can say:

• Length = 6 × Width

Now using the perimeter:

• 2(6 × Width + Width) = 56

Simplify and solve for Width:

• 2(7 × Width) = 56
• 14 × Width = 56
• Width = 56 / 14
• Width = 4 inches

Now we can find the Length by multiplying the width by 6:

• Length = 6 × 4
• Length = 24 inches

The dimensions of the rectangle are a length of 24 inches and a width of 4 inches.

Answer 2

lets use width=w and length=l
we know that 2w+2l = 56, and that 6l=1w
since the second equation is already solved for w, we can plug that into the first equation, giving 2(6l)+2l=56.
solving for l will give us 12l+2l=56 => 14l=56 => l=56/14=4
with l=4, we can find the width using the second equation.
6(4)=w
w=24
Final answer:
The length is 4 inches and the width is 24 inches.
Hope I helped :)