The base of the triangle is 5 cm greater than the height. The area is 33 cm^2. Find the height and the length of the base.
The height of the triangle is ___ cm
The base of the triangle is ___ cm
b = 5 + h
b (h/2) = 33
b h = 66
(5+h)h = 66
h^2 + 5 h - 66 = 0
(h - 6)(h+11) = 0
h = 6
b = 11
Why did the triangle go to therapy? Because it had some serious base issues!
Alright, let's solve this triangle puzzle together.
Let's assume the height of the triangle is "h" cm. According to the given information, the base is 5 cm greater than the height, so the length of the base is "h + 5" cm.
Now, we know that the area of a triangle is given by the formula: (base * height) / 2.
So, in this case, the area is 33 cm^2. Plugging in the values, we get:
( (h + 5) * h ) / 2 = 33
Simplifying, we have:
(h^2 + 5h) / 2 = 33
Cross-multiplying, we get:
h^2 + 5h = 66
Rearranging the equation, we have:
h^2 + 5h - 66 = 0
Now, we can solve this quadratic equation. Factoring or using the quadratic formula, we find that the solutions to this equation are h = -11 and h = 6. Since a negative height doesn't make sense in this context, we ignore the negative value.
Therefore, the height of the triangle is 6 cm.
To find the length of the base, we can substitute h = 6 into our earlier equation:
Base = 6 + 5 = 11 cm.
So, the height of the triangle is 6 cm, and the length of the base is 11 cm.
Let's assume the height of the triangle is 'h' cm.
According to the given information, the base of the triangle is 5 cm greater than the height. Therefore, the length of the base is 'h + 5' cm.
The area of a triangle can be calculated using the formula:
Area = (1/2) * base * height
Substituting the given values:
33 cm^2 = (1/2) * (h + 5) cm * h cm
Now we can solve for 'h' by simplifying the equation and solving the quadratic equation:
33 = (1/2) * (h^2 + 5h)
66 = h^2 + 5h
h^2 + 5h - 66 = 0
Factoring this quadratic equation, we get:
(h - 6)(h + 11) = 0
Therefore, the possible solutions are:
h - 6 = 0 or h + 11 = 0
Solving these equations separately, we find:
h = 6 or h = -11
Since height cannot be negative, the height of the triangle is 6 cm.
Now we can find the base of the triangle:
base = h + 5 = 6 + 5 = 11 cm
Therefore, the height of the triangle is 6 cm and the length of the base is 11 cm.
To find the height and length of the base of the triangle, we can use the formula for the area of a triangle:
Area = (base * height) / 2
Given that the area is 33 cm^2, we can rewrite the formula as:
33 = (base * height) / 2
Next, we are given that the base of the triangle is 5 cm greater than the height. We can represent this relationship as:
base = height + 5
Substituting this expression for base into the equation, we have:
33 = ((height + 5) * height) / 2
To solve this equation for the height, we can multiply both sides by 2 to get rid of the fraction:
66 = (height + 5) * height
Expanding the equation, we have:
66 = height^2 + 5height
Rearranging the equation to make it a quadratic equation, we have:
height^2 + 5height - 66 = 0
Now we can solve this equation by factoring or using the quadratic formula. Let's use factoring:
(height + 11)(height - 6) = 0
Setting each factor equal to zero, we have:
height + 11 = 0 or height - 6 = 0
Solving for height in each equation, we get:
height = -11 or height = 6
Since the height of a triangle cannot be negative, we can discard the negative value. Therefore, the height of the triangle is 6 cm.
To find the length of the base, we can substitute the value of height into the expression for base:
base = height + 5 = 6 + 5 = 11 cm
So, the height of the triangle is 6 cm and the base of the triangle is 11 cm.