Math plz help me

Question

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

Answer 1

I suppose the triangular flag is measure within x-y plane, so the length = base and the width = height

Let x be the width

Then, we will know that the area of triangular flag is:

A = (1/2)(base)(height) = (1/2)(4x)(x) = 72

x² = 36

x = 6 (Thus, height = 6 feet, base = 4(6) = 24 feet)

Then, for rectangular mat, we will have A = (14 + x)(x) = 72

x² + 14x - 72 = 0

(x + 18)(x - 4) = 0

x = 4 (Thus, width = 4 feet, length = 14 + 4 = 18 feet)