The perimeter of an isosceles triangle is 32 cm. the base is 2 cm longer than the length of one of the congruent sides. What is the area of the triangle?
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Let (x) represent the length of one of the congruent sides of the isosceles triangle.
The base of the triangle is (x + 2) since it is 2 cm longer than one of the congruent sides.
The perimeter of the triangle is the sum of all three sides, which is (2x + (x + 2) = 32).
Solve the equation for (x) to find the length of one of the congruent sides.
Once you have found (x), you can use the formula for the area of a triangle, which is (\frac{1}{2} \times \text{base} \times \text{height}), where the height can be found using Pythagoras theorem or by dropping a perpendicular from the apex of the triangle to the base.
Calculate the area of the triangle using the values you found for the base and height.
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To find the area of the triangle, we first need to find the lengths of the sides. Let x be the length of one congruent side.
Since the base is 2 cm longer than one congruent side, the length of the base is x + 2 cm.
The perimeter of the triangle is the sum of the lengths of all three sides, which is:
Perimeter = x + x + (x + 2) = 32 cm
Solving for x:
3x + 2 = 32 3x = 30 x = 10
So, the length of one congruent side is 10 cm, and the length of the base is 12 cm.
Now, we can use Heron's formula to find the area of the triangle:
Area = √[s(s - a)(s - b)(s - c)]
Where s is the semi-perimeter of the triangle, and a, b, and c are the lengths of the sides.
Semi-perimeter (s) = (10 + 10 + 12) / 2 = 16 cm
Now, plugging the values into the formula:
Area = √[16(16 - 10)(16 - 10)(16 - 12)]
Area = √[16(6)(6)(4)]
Area = √[2304]
Area ≈ 48 cm²
Therefore, the area of the triangle is approximately 48 square centimeters.
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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.
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