the hight of a triangle is four times the length of the base. find the base and height of the triangle if the area is 18 square inches?

let the base be x units long, where x is a positive number

then the height is 4x units long

Area of triangle = 1/2 base x height
18 = 1/2(x)(4x)
9 = x^2
x = 3

so .....

To find the base and height of the triangle, we need to solve a system of equations based on the given information. Let's denote the length of the base as 'b' and the height as 'h'.

We are given that the height of the triangle is four times the length of the base:
h = 4b (Equation 1)

The formula for the area of a triangle is (1/2) * base * height. We are given that the area is 18 square inches:
(1/2) * b * h = 18 (Equation 2)

To solve this system of equations, we will substitute Equation 1 into Equation 2.

Substituting h = 4b in Equation 2:
(1/2) * b * (4b) = 18
2b^2 = 18
b^2 = 9
b = √9
b = 3

Now, substitute the value of b back into Equation 1 to find the height:
h = 4(3)
h = 12

Therefore, the base of the triangle is 3 inches and the height is 12 inches.