# Two sides of a triangle are equal in length. The base of the triangle (the side that isn't equal in length to the other two) measures #7.6# cm. The two equal sides both measure #5# cm. What is the area of the triangle?

12.35

With two sides of equal length, this is an isosceles triangle. Thus the line from the apex to the base will divide the lower side exactly in half (3.8). Then we can use the equation for the area of a triangle, where the height is calculated from the Pythagorean Theorem.

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The area is approximately

We'll keep that as an exact value for now.

However, we have two of these triangles, so the total area is

Hopefully this helps!

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To find the area of the triangle, you can use the formula for the area of a triangle, which is: Area = (base × height) / 2. In this case, since you have an isosceles triangle (two sides of equal length), you can draw a perpendicular line from the apex (top) of the triangle to the base, creating two right-angled triangles.

Using the Pythagorean theorem, you can find the height of one of these right-angled triangles. Let's call the height h. Since the triangle is isosceles, the height divides the base into two equal segments.

Given that the base (b) is 7.6 cm and the two equal sides (a) are 5 cm each, you can use the Pythagorean theorem to find the height:

h^2 = a^2 - (b/2)^2 h^2 = 5^2 - (7.6/2)^2 h^2 = 25 - 14.4^2 h^2 = 25 - 29.16 h^2 = -4.16 (Discard negative value as it's not possible)

Since the height cannot be negative, there is no real solution for h in this case, indicating that the given measurements do not form a valid triangle. Therefore, the area cannot be calculated.

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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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