Question

The base of a triangle is √20 cm and its height is√8 cm. Find its area. Write your answer in simplified radical form.

Answer 1

Answer: the area of the triangle is (1/2) * √20 cm

Step-by-step explanation:

The area of a triangle is equal to one half of the product of the base and the height. In this case, the base of the triangle is √20 cm and the height is √8 cm, so we can find the area by doing this:

Area = (1/2) * (√20 cm) * (√8 cm)

To simplify this expression, we can first multiply the numerator and denominator by the square root of the denominator:

Area = (1/2) * (√20 cm * √8 cm) / (√8 cm)

This gives us:

Area = (1/2) * (√160 cm^2) / (√8 cm)

Now we can cancel out the square root of 8 in the numerator and denominator:

Area = (1/2) * √160 cm^2 / √8 cm

Area = (1/2) * √20 cm

Thus, the area of the triangle is (1/2) * √20 cm, which is the simplified radical form of the answer.

Answer 2

Answer:
`2√(10) \ \ \text{square cm}`

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Work Shown:

`\text{area} = 0.5*\text{base}*\text{height}\\\\\text{area} = 0.5*√(20)*√(8)\\\\\text{area} = 0.5*√(20*8)\\\\\text{area} = 0.5*√(160)\\\\\text{area} = 0.5*√(16*10)\\\\\text{area} = 0.5*√(16)*√(10)\\\\\text{area} = 0.5*4*√(10)\\\\\text{area} = 2√(10)\\\\`

The area units are in square centimeters.

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Step-by-step explanation:

As the steps above indicate, I used this rule

`√(A*B) = √(A)*√(B)`

This is to combine the roots in the 3rd step, but also to pull them apart in the 6th step. The idea is to pull out the largest perfect square factor to simplify the square root.