The base of a triangle is 6cm greater than the height. The area is 20cm^2. Find the height and the length of the base.

The base of a triangle is 6cm greater than the height. The area is 20cm^2. Find the height and the length of the base.

Put your question in the search box in Google and it will show you the answer and the explanation how to get the answer. Believe me. I know ! Good Luck! :)

To find the height and the length of the base of the triangle, we will set up an equation based on the given information.

Let's assume that the height of the triangle is 'h' cm. According to the given information, the base of the triangle is 6 cm greater than the height, so the length of the base can be represented as 'h + 6' cm.

The formula for the area of a triangle is A = (1/2) × base × height. We are given that the area is 20 cm².

Substituting the given values into the formula, we have:

20 = (1/2) × (h + 6) × h

Now, we can simplify the equation and solve for 'h':

20 = (1/2) × (h² + 6h)

Multiplying both sides of the equation by 2 to eliminate the fraction:

40 = h² + 6h

Rearranging the equation to have it set equal to zero:

h² + 6h - 40 = 0

Now, we can solve this quadratic equation by factoring or using the quadratic formula. Let's use the quadratic formula:

h = [-b ± √(b² - 4ac)] / (2a)

For our quadratic equation h² + 6h - 40 = 0, the values of a, b, and c are:

a = 1
b = 6
c = -40

Substituting these values into the quadratic formula, we get:

h = [-6 ± √(6² - 4(1)(-40))] / (2(1))

Simplifying further:

h = [-6 ± √(36 + 160)] / 2

h = [-6 ± √196] / 2

Now, we evaluate the square root:

h = (-6 ± 14) / 2

This gives us two possible values for 'h':

h₁ = (-6 + 14) / 2 = 8 / 2 = 4
h₂ = (-6 - 14) / 2 = -20 / 2 = -10

Since the height of a triangle cannot be negative, we discard the negative solution.

So, the height of the triangle is 4 cm.

Now, we can find the length of the base by substituting this value back into our initial expression for the base:

base = height + 6
base = 4 + 6
base = 10 cm

Therefore, the height of the triangle is 4 cm, and the length of the base is 10 cm.