# The ratio of the length (including the endzone) to the width of an NFL football field is 2.25. If the perimeter of the football field is 1040 feet, what are the dimensions of the field?

Question
Performing transformations
The ratio of the length (including the endzone) to the width of an NFL football field is 2.25. If the perimeter of the football field is 1040 feet, what are the dimensions of the field?

2020-10-27
Let l be the length and w be the width so that the perimeter is: P=2l+2w
We find an expression for l in terms of w using the given perimeter: 1040=2l+2w
Divide both sides by 2: 520=l+w
520-w=l
The ratio of the length to the width is 2.25: l/w=2.25
$$\displaystyle\frac{{{520}-{w}}}{{w}}={2.25}$$
Multiply both sides by 2.25: 520-w=2.25w
Add w to both sides: 520=3.25w
Divide both sides by 3.25: 160=w
Solve for l using (1): l=520-160
l=360
So, the dimentions of the field are 360 feet by 160 feet

### Relevant Questions

The garden is made up of a rectangular patch of grass and two semi-circular vegetable patches. If the dimensions of the rectangular patch are 16 m (length) and 8 m (width) respectively, calculate: a) the perimeter of the garden.
b) the total area of the garden.
Suppose electrons enter the uniform electric field midwaybetween two plates, moving at an upward 45 degree angle as shown.What maximum speed can the electrons have if they are to avoidstriking the upper plate. Ignore fringing of the field. Upper plate is negatively charged bottom plate is positivelycharged length of plate is 6cm and distance from top of top plateto bottom of bottom plate is 1cm.
$$\displaystyle{E}={5.0}\times{10}^{{3}}\frac{{N}}{{C}}$$
A person holds a book 25 cm in front of the effective lens ofher eye; the print in the book is 2.5mm high. If the effective lens of the eye is located 1.7 cm fromthe retina, what is the size (including the sign) of the printimage on the retina?
In the arrangement shown in Figure P14.40, an object of mass,m = 2.0 kg, hangs from a cordaround a light pulley. The length of the cord between pointP and the pulley is L = 2.0 m.(a) When thevibrator is set to a frequency of 145Hz, a standing wave with six loops is formed. What must be thelinear mass density of the cord in kg/m? (b) How many loops (ifany) will result if m is changed to 2.88 kg?
(c) How many loops (if any) will result if m is changed to72.0 kg?
A 75.0-kg man steps off a platform 3.10 m above the ground. Hekeeps his legs straight as he falls, but at the moment his feettouch the ground his knees begin to bend, and, treated as aparticle, he moves an additional 0.60 m before coming torest.
a) what is the speed at the instant his feet touch theground?
b) treating him as a particle, what is his acceleration(magnitude and direction) as he slows down, if the acceleration isassumed to be constant?
c) draw his free-body diagram (see section 4.6). in termsof forces on the diagram, what is the net force on him? usenewton's laws and the results of part (b) to calculate the averageforce his feet exert on the ground while he slows down. expressthis force in newtons and also as a multiple of his weight.
a)
b)
Figure shows a nonconducting rod with a uniformly distributed charge +Q. The rod forms a 10/22 of circle with radius R and produces an electric field of magnitude Earc at its center of curvature P. If the arc is collapsed to a point at distance R from P, by what factor is the magnitude of the electric field at P multiplied?
A square loop of copper wire is initially placed perpendiclar to the lines of a constant magnetic field of $$\displaystyle{5}\times{10}^{{3}}$$ T.The area enclosed by the loop is 0.2 square meter. the loopis then turned through an angle $$\displaystyle{90}^{\circ}$$ so thatthe plane of the loop is parallel to the field lines. the turntakes 0.1 second. what is the average emf induced in the loop during the turn?
An airplane propeller is 2.08 m in length (from tip to tip) and has a mass of 117 kg. When the airpline's engine is first started, it applies a constant torque of $$\displaystyle{1950}\ {N}\cdot{m}$$ to the propeller, which starts from rest.