Answer:
The width is 5 inches and the height is 18 inches.
Step-by-step explanation:
The area of a triangle can be calculated as:
A = w*h/2
where w is the width of the base, and h is the height.
then we have that:
w*h/2 = 45 in^2
and the height is 2 less than 4 times the width.
h = 4*w - 2in
then we have a system with 2 equations:
w*h/2 = 45 in^2
h = 4*w - 2in
We can replace the second one in the first one and solve it for w.
w*(4*2 - 2in)/2 = 45 in^2
2w^2 - w = 45in^2
2w^2 - w - 45in = 0
then we have to solve the quadratic equation:
the solutions are:
w = (1 +- √(1^2 - 4*2*(-45))/(2*2) = (1 + - √361)/4
where we have two solutions for w, one for each sign of the square root.
we obviously need to take the positive solution (because we can not have a negative length)
w = (1 + √361)/4 = 5in
now, we can replace it in the equation "h = 4*w - 2in" to get the height.
h = 4*5in - 2in = 18in
