Question 1130918
the area of the screen is 7500 square meters.
the length is 10 meters more than eight times its width.


let L = the length and W = the width.


the formula for area of the rectangle is L * W = the area.


since the area is 7500 square meters, the formula becomes L * W = 7500


since the length is 10 meters more than eight times the width, then:


L = 8 * W + 10


the formula for area of L * W = 7500 becomes:


(8 * W + 10) * W = 7500, after your replace L with its equivalent value of 8 * W + 10


simplify (8 * W + 10) * W = 7500 to get 8 * W^2 + 10 * W = 7500


subtract 7500 from both sides of the equation to get 8 * W^2 + 10 * W - 7500 = 0


factor this quadratic equation to get W = -31.25 or W = 30


W can't be negative, so W must be equal to 30.


L = 8 * W + 10, so L = 8 * 30 + 10 = 250.


the length of the screen is 250 meters and the width of the screen is 30 meters.


the area of the screen is 250 * 30 = 7500 square meters.


solution looks good.


you could have also simplified the quadratic equation before solving to get:


8 * W^2 + 10 * W - 7500 = 0 becomes 4 * W^2 + 5 * W - 3750 = 0.


the solution would have been the same.


the problem was solved using the quadratic formula.


the width was 30.


the length was 250, which is 8 * 30 + 10.