Answer
The width of the football field is $53$ meters and the length is $120$ meters.
Work Step by Step
We know that the perimeter of a rectangle is given by the following formula:
$$P = 2l + 2w$$
We know that the perimeter is $346$ meters, We also know that the length is $14$ meters longer than twice the width.
If $w$ is the measure of the width, then let $2w + 14$ be the measure of the length of this football field.
We can now plug in this information into the formula for perimeter:
$$346 = 2(2w + 14) + 2w$$
Use distributive property:
$$346 = 4w + 28 + 2w$$
Combine like terms:
$$6w + 28 = 346$$
Subtract $28$ from each side of the equation to isolate the variable:
$$6w = 318$$
Divide each side by $6$ to solve for $w$:
$$w = 53$$
We know that the length $l$ is $14$ more than twice the width $w$, we can use this information to solve for $l$:
$$l = 2(53) + 14$$
Multiply first according to order of operations:
$$l = 106 + 14$$
Now we can add:
$$l = 120$$
The width of the football field is $53$ meters and the length is $120$ meters.
