Question

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

Answer 1

Answer:

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

$l = 4w$,

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

$A =\dfrac{lw}{2} = \dfrac{w(4w)}{2}=72ft^2$

solving for width $w$ we get:

$w = \sqrt{\dfrac{72}{2}},$

$\boxed{w = 4\: feet}$

which gives a length of

$l= 4w = 4*6ft$

$\boxed{l= 24\: feet.}$

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

$l_1 = w_1+14$

and its area is 72 square feet which means

$A = l_1w_1 = (w_1+14)w_1 = 72ft^2$

simplification gives

$w_1^2+14w_1-72=0$

which we solve using the quadratic formula to give

$\boxed{w_1= 4ft}$,

$w_1 = -18ft$,

and since the width cannot be a negative number, we choose $w_1= 4ft$ as our answer.

Thus, the length of the rectangular box is

$l_1 = w_1+14 = 4+14\\\\ \boxed{l_1 = 18\: feet.}$

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.