Final answer:
The height of the triangle can be found by setting up an equation using the given information and solving for the base. The base is then substituted into the expression for the height to find the actual height of the triangle.
Step-by-step explanation:
To find the height of the triangle, we need to set up an equation using the information given in the problem.
Let's assume the base of the triangle is x feet. According to the problem, the height of the triangle is 3 feet less than its base, so the height would be (x - 3) feet.
We also know that the area of the triangle is 35ft². The formula for the area of a triangle is A = 1/2bh, where A is the area, b is the base, and h is the height. Plugging in the given values, we get:
35 = 1/2 * x * (x - 3)
Now we can solve for x:
70 = x^2 - 3x
x^2 - 3x - 70 = 0
Using the quadratic formula or factoring, we find that x = 10 or x = -7. Since we're dealing with a measurement of length, we can ignore the negative value and conclude that the base of the triangle is 10 feet.
Substituting x = 10 into the expression for the height, we find that the height of the triangle is 10 - 3 = 7 feet.