Answer:
Let x be the length of the base of the triangle, then the height h is given by h = 2x - 3 (since the height is 3 inches less than twice the length of the base).
The area of a triangle is given by the formula A = (1/2)bh, where b is the base and h is the height. We are given that the total area of the triangle is 7 square inches, so we can write:
(1/2)(x)(2x - 3) = 7
Multiplying both sides by 2 to eliminate the fraction, we get:
x(2x - 3) = 14
Expanding the left side, we get:
2x^2 - 3x = 14
Subtracting 14 from both sides, we get:
2x^2 - 3x - 14 = 0
We can now use the quadratic formula to solve for x:
x = (-b ± sqrt(b^2 - 4ac))/(2a)
where a = 2, b = -3, and c = -14. Plugging in these values, we get:
x = (-(-3) ± sqrt((-3)^2 - 4(2)(-14)))/(2(2))
= (3 ± sqrt(169))/4
= (3 ± 13)/4
Taking the positive value for x (since the length of the base must be positive), we get:
x = (3 + 13)/4
= 4
Therefore, the length of the base is 4 inches. To find the height h, we can use the formula h = 2x - 3:
h = 2(4) - 3
= 5
So the height of the triangle is 5 inches.