# The base of a triangle is 4 cm greater than the height. The area is 30 cm^2. How do you find the height and the length of the base?

Height is

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Let h represent the height of the triangle. The base of the triangle is then h + 4. Using the formula for the area of a triangle, A = (1/2) * base * height, we can plug in the given values for the area and the expressions for the base and height:

30 = (1/2) * (h + 4) * h

Now, solve for h:

30 = (1/2) * (h^2 + 4h) 60 = h^2 + 4h 0 = h^2 + 4h - 60

Using the quadratic formula, h = (-b ± √(b^2 - 4ac)) / (2a), where a = 1, b = 4, and c = -60:

h = (-4 ± √(4^2 - 4(1)(-60))) / (2(1)) h = (-4 ± √(16 + 240)) / 2 h = (-4 ± √256) / 2 h = (-4 ± 16) / 2

Now, we have two possible solutions for h:

h₁ = (-4 + 16) / 2 = 6 h₂ = (-4 - 16) / 2 = -10

Since the height cannot be negative, we discard h₂ and conclude that the height of the triangle is 6 cm.

To find the length of the base, we use the expression h + 4:

base = 6 + 4 = 10 cm.

Therefore, the height of the triangle is 6 cm and the length of the base is 10 cm.

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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