the height of a triangle is 4 centimeters longer than its base. If the area of the triangle is 22.5 swuare centimeters, then what is the height of the triangle?

okay, so the base of the triangle is (b).

that means the height of the triangle will be (b+4).
since the area of a triangle is (basexheight) and the area is already given as 22.5, then you can find (b) by plugging in the area formula.

(b) x (b+4)= 22.5
b^2 + 4b= 22.5
b^2 + 4b - 22.5= 0

solve by quadratic formula.
**the answer is the positive number, because you can't have a triangle with a side of negative centimeters.

A=1/2bh=1/2 (b)(b+4)

22.5=1/2 (b2+4b)
45=b2+4b
b2+4b-45=0
(b-5)(b+9)=0
b-5=0
b=5
h=b+4=5+4=9

ack. just remembered area of a triangle is (basexheight/2). that makes things easier, and Mary is right.

To find the height of the triangle, we'll first use the formula for the area of a triangle, which is:

Area = (1/2) * base * height

Given that the area of the triangle is 22.5 square centimeters, we can substitute this value into the equation:

22.5 = (1/2) * base * height

Now, we know that the height of the triangle is 4 centimeters longer than its base. Let's represent the base as 'b'. Therefore, the height would be 'b + 4'.

Replacing height with 'b + 4', we get:

22.5 = (1/2) * b * (b + 4)

To simplify the equation, let's multiply both sides by 2 to get rid of the fraction:

45 = b * (b + 4)

Expanding the equation:

45 = b^2 + 4b

Rearranging the equation and setting it equal to zero:

b^2 + 4b - 45 = 0

Now, we can solve this quadratic equation by factoring or using the quadratic formula. Factoring this equation, we have:

(b + 9)(b - 5) = 0

Setting each factor equal to zero, we get:

b + 9 = 0 or b - 5 = 0

Solving these equations, we find that:

b = -9 or b = 5

Since the base of a triangle cannot be negative, we discard the solution b = -9.

Therefore, the base of the triangle is 5 centimeters.

Finally, we can substitute the value of the base back into the equation for the height:

height = base + 4 = 5 + 4 = 9 centimeters

So, the height of the triangle is 9 centimeters.