Question

A rectangle has perimeter of 58 inches. The length is one more than 3 times the width. Write and solve a system of linear equations to find the length of the rectangle.

Answer 1

Answer:

First write equations for what you know: A perimeter is the distance around the rectangle, there are 2 lengths and 2 widths, we know the perimeter is 58 inches..So...

2L + 2W = 58 this is equation 1

Next we know that the length is one more than 3 times the width..so..

L = 3W + 1 equation 2

Since we know that L = 3W + 1 we can substitute the L in equation 1

2(3W + 1) + 2W = 58 solve the problem

6W + 2 + 2W = 58 add the common terms

8W + 2 = 58 subtract 2 from both sides

8W = 56 divide by 8

W = 7

Now that you know W, go back and solve for L....use equation 2

L = 3(7) + 1

L + 21 + 1

L = 22

hope this helps