Question

The length of a rectangle is equal to triple the width. Which system of equations can be used to find the dimensions of the rectangle if the perimeter is 86 centimeters

Answer 1

To determine the rectangle's dimensions with a perimeter of 86 cm and a length three times its width, we use a system of equations. The width is calculated to be 10.75 cm and from there, we calculate the length to be 32.25 cm.

Step-by-step explanation:

To find the dimensions of a rectangle where the length is triple the width and the perimeter is 86 centimeters, we can set up a system of equations. Let's denote the width as w and the length as l. Since the length is equal to triple the width, we have l = 3w. The formula for perimeter P of a rectangle is given by P = 2l + 2w. Substituting the perimeter given and the relationship between length and width, we can write the equations as:

• l = 3w
• 2l + 2w = 86

By substituting the first equation into the second, we get:

• 2(3w) + 2w = 86
• 6w + 2w = 86
• 8w = 86
• w = 86 / 8
• w = 10.75 cm

Then, using the first equation, we find the length:

• l = 3(10.75)
• l = 32.25 cm

Thus, the width is 10.75 centimeters, and the length is 32.25 centimeters.

Answer 2

w=10.75 l=32.25

Step-by-step explanation:

So if we know that the length is 3 times as long as the width than if the width is x, length would be 3x.

3x+3x+x+x=86 There are two lengths and two widths

8x=86 Combine like terms

x=10.75 divide both sides by 8 and our width is 10.75

Length is 32.25 multiply 10.75 by 3