The height of a triangle is 4 inches more than the base. The area of the triangle is 35 square inches. Find the base and height of the triangle.
b(b+4)/2 = 35
To find the base and height of the triangle, we need to set up an equation using the given information.
Let's represent the base of the triangle as "b" inches.
According to the given information, the height of the triangle is 4 inches more than the base. So, the height can be represented as "b + 4" inches.
The formula for the area of a triangle is 1/2 * base * height. Here, the area is given as 35 square inches.
Using this information, we can set up the equation:
1/2 * b * (b + 4) = 35
To solve this equation for the base and height, we can simplify and solve for "b".
Let's simplify the equation:
(b^2 + 4b)/2 = 35
b^2 + 4b = 70
Rearranging the equation:
b^2 + 4b - 70 = 0
Now we have a quadratic equation that can be solved for the base, "b".
To find the values of "b", we can either factor the quadratic equation or use the quadratic formula.
Let's use the quadratic formula:
The quadratic formula states that for an equation of the form ax^2 + bx + c = 0, the solutions for x can be found using the formula:
x = (-b ± √(b^2 - 4ac)) / 2a
In our equation, a = 1, b = 4, and c = -70.
Substituting these values into the quadratic formula:
b = (-4 ± √(4^2 - 4(1)(-70))) / (2*1)
Simplifying further:
b = (-4 ± √(16 + 280)) / 2
b = (-4 ± √296) / 2
Now, we can find the two possible values for the base, "b".
b = (-4 + √296) / 2 ≈ 5.69
b = (-4 - √296) / 2 ≈ -9.69
Since the base of a triangle cannot be negative, we discard the negative value.
Therefore, the base of the triangle is approximately b = 5.69 inches.
To find the height, we can substitute this value back into the equation for the height:
Height = b + 4 ≈ 5.69 + 4 ≈ 9.69 inches
Therefore, the base of the triangle is approximately 5.69 inches and the height is approximately 9.69 inches.