The base of a triangle is 8cm greater than the height. The area is 42cm^2. Find the height and length of the base.
base 8 and height 12???
Let's assume that the height of the triangle is represented by "h" cm.
According to the given information, the base of the triangle is 8 cm greater than the height, so the base can be represented by "h + 8" cm.
The formula to calculate the area of a triangle is:
Area = (1/2) x base x height
Substituting the given area and the corresponding values in the formula, we have:
42 cm^2 = (1/2) x (h + 8) cm x h cm
Expanding the equation, we have:
42 = (1/2) x (h^2 + 8h)
Simplifying further:
42 = (1/2)h^2 + 4h
Multiplying the entire equation by 2 to remove the fraction:
84 = h^2 + 8h
Rearranging the equation:
h^2 + 8h - 84 = 0
To solve this quadratic equation, we can factorize it:
(h + 14)(h - 6) = 0
Therefore, the possible values for h are -14 and 6. Since the height cannot be negative, we discard -14.
So, the height of the triangle is 6 cm.
To find the length of the base, we substitute the height value back into the given equation:
base = height + 8
base = 6 cm + 8 cm
base = 14 cm
Hence, the height of the triangle is 6 cm, and the length of the base is 14 cm.
To solve this problem, we can use the formula for the area of a triangle:
Area = (1/2) * base * height
Given that the area is 42 cm², we can substitute this value into the formula:
42 = (1/2) * base * height
We are also given that the base of the triangle is 8 cm greater than the height. Let's call the height h. Then the base would be h + 8.
Substituting this into the equation, we get:
42 = (1/2) * (h + 8) * h
Now, let's solve for h.
Multiply both sides of the equation by 2:
84 = (h + 8) * h
Expand the right side of the equation:
84 = h² + 8h
Rearrange the equation to form a quadratic equation:
h² + 8h - 84 = 0
To solve this quadratic equation, we can factor it or use the quadratic formula. Let's factor it:
(h - 6)(h + 14) = 0
Setting each factor equal to zero, we find two possible values for h:
h - 6 = 0 --> h = 6
or
h + 14 = 0 --> h = -14
Since the height of a triangle cannot be negative, we discard the solution h = -14.
Therefore, the height of the triangle is 6 cm.
The base of the triangle is 8 cm greater than the height, so the base would be 6 + 8 = 14 cm.
Thus, the height is 6 cm and the length of the base is 14 cm.
Area of triangle = 1/2(height x base)
The problem states that base is 8 cm greater than the height; therefore, base-8 = height.
A = 1/2(b*h)
42 = 1/2(b*[b-8])
84=(b^2-8b)
rearrange to
b^2 - 8b -84
factor to
(b+8)(b-14)
Therefore, b = -8 cm which makes no sense and
b = +14 cm
and height = 14-8 = 6
Check:
1/2(b*h) = area
1/2(14*6) = 1/2(84)=42
Check my work.