A triangular flag is 4 times as long as its width. A rectangular mat is 14 feet longer than its width. Both the flag and the mat have an area of 72 square feet. Find the base and height of the flag

For the triangle: length = 24ft, width = 6ft.

For the rectangular mat: length = 18ft, width = 4ft.

Step-by-step explanation:

A triangular flag is 4 times as long as its width, meaning

,

and the area of the this flag is 72 square feet, which means

solving for width we get:

which gives a length of

Similarly, rectangular mat is 14 feet longer than its width, meaning

and its area is 72 square feet which means

simplification gives

which we solve using the quadratic formula to give

,

,

and since the width cannot be a negative number, we choose as our answer.

Thus, the length of the rectangular box is

To summarize, the length and the width of the triangular flag is 24 and 6 feet respectively, and for the rectangular box it is 18 and 4 feet respectively.