COULD SOMEONE PLEASE HELP ME WITH THIS !!!!!!!!!!
The base of a triangle is 3cm greater than the height. The area is 44cm^2. Find the height and length of the base.
The height of the triangle is_______ cm
The base of the traingle is_______cm
To find the height and length of the base of the triangle, we can use the formula for the area of a triangle which is:
Area = (base * height) / 2
Given that the area is 44 cm², we can substitute this value into the formula. Let's call the height "h" and the base "b+3" (as it is 3 cm greater than the height). So the equation becomes:
44 = ((b+3) * h) / 2
To solve for the two unknowns, we need another equation relating the height and the base. We know that the base is 3 cm greater than the height, so we can write:
b = h + 3
Now we can substitute this expression for the base (b) in the previous equation:
44 = ((h+3+3) * h) / 2
Simplifying this equation, we get:
44 = (h+6) * h / 2
Multiplying both sides of the equation by 2:
88 = (h+6) * h
Expanding the equation:
88 = h² + 6h
Rearranging the terms:
h² + 6h - 88 = 0
Now we have a quadratic equation. We can factorize it or use the quadratic formula to find the values of h. By factoring or using the quadratic formula, we find two possible values for h:
h = -11 or h = 8
Since a negative height doesn't make sense in this context, we can discard the negative value.
Therefore, the height of the triangle is 8 cm.
Substituting this value back into the equation for the base:
b = h + 3
b = 8 + 3
b = 11
So, the base of the triangle is 11 cm.
(1/2) b h = 44
so
b h = 88
but b = h + 3
so
(h+3)h = 88
h^2 + 3 h - 88 = 0
(h-8)(h+11) = 0
h = 8
take it from there