the height of a tringle is 3 ft longer then the base. the area of the trianlge is 35 sqft. find the hight and base of the triangel.
To find the height and base of the triangle, we can use the formula for the area of a triangle: A = (1/2) × base × height.
Given that the height of the triangle is 3 ft longer than the base and the area of the triangle is 35 sqft, we can set up the equation as:
35 = (1/2) × base × (base + 3)
Let's solve this equation to find the base and height.
Step 1: Simplify the equation.
35 = (1/2) × (base^2 + 3base)
Step 2: Distribute (1/2) to both terms inside the parentheses.
35 = (1/2) × base^2 + (1/2) × 3base
Step 3: Simplify further.
35 = (1/2) × base^2 + (3/2) × base
Step 4: Multiply both sides of the equation by 2 to eliminate the (1/2) term.
70 = base^2 + 3base
Step 5: Rearrange the equation to set it equal to zero.
base^2 + 3base - 70 = 0
Step 6: Factorize the quadratic equation or use the quadratic formula. In this case, let's factorize it.
(base - 7)(base + 10) = 0
This gives us two possibilities:
1. base - 7 = 0, which means base = 7
2. base + 10 = 0, which is not possible since the base cannot be negative.
Thus, the base of the triangle is 7 ft.
Step 7: Calculate the height using the base value.
Since the height is 3 ft longer than the base, we can calculate it as:
height = base + 3
height = 7 + 3
height = 10
Therefore, the height of the triangle is 10 ft and the base is 7 ft.