a triangle has an area of 35 square inches, and its base is 3 inches more than it's height. Find the base and height of the trianlge
Area of a triangle:
A = b * h / 2
A triangle base is 3 inches more than it's height.
This mean : b = h + 3
A = b * h / 2 = ( h + 3 ) * h / 2 = 35 in ^ 2
( h * h + 3 * h ) / 2 = 35
( h ^ 2 + 3 h ) / 2 = 35 Multiply both sides by 2
h ^ 2 + 3 h = 70 Subtract 70 to both sides
h ^ 2 + 3 h - 70 = 70 - 70
h ^ 2 + 3 h - 70 = 0
The solutions are :
h = - 10
and
h = 7
Height can't be negative so :
h = 7 in
b = h + 3 = 7 + 3 = 10 in
A = 10 * 7 / 2 = 70 / 2 = 35 in ^ 2
To find the base and height of the triangle, we can use the formula for the area of a triangle, which is given by:
Area = (1/2) * base * height
In this case, the area of the triangle is given as 35 square inches. Let's assume that the height of the triangle is represented by the variable 'h.'
We are also given that the base of the triangle is 3 inches more than its height. Therefore, we can represent the base as 'h + 3.'
Substituting these values into the area formula, we have:
35 = (1/2) * (h + 3) * h
To simplify the equation, let's multiply both sides by 2 to remove the fraction:
70 = (h + 3) * h
Expanding the right side, we have:
70 = h^2 + 3h
Rearranging the equation in standard quadratic form, we get:
h^2 + 3h - 70 = 0
Now, we can solve this quadratic equation for the value of 'h' using factoring, completing the square, or the quadratic formula. In this case, let's use factoring to find the factors of -70 that add up to 3:
(h - 7)(h + 10) = 0
Setting each factor equal to zero, we have:
h - 7 = 0 or h + 10 = 0
Solving for 'h' in each equation, we get:
h = 7 or h = -10
Since the height of the triangle cannot be negative, we discard h = -10.
So, the height of the triangle is 7 inches.
Now, we can substitute this value back into the expression for the base:
Base = height + 3 = 7 + 3 = 10 inches
Therefore, the base and height of the triangle are 10 inches and 7 inches, respectively.