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vova2212 [387]
3 years ago
9

Which rectangular prism will have the largest volume?

Mathematics
1 answer:
djverab [1.8K]3 years ago
5 0

Answer:

The rectangular prism with these dimensions w = 3 cm, l = 5 cm, h = 5 cm has the largest volume.

Step-by-step explanation:

The formula for the Volume of a V = 3 * 5 * 5

V = l * w * h

V = 3 * 5 * 5

V = 75 cm³

The rectangular prism with these dimensions w = 3 cm, l = 5 cm, h = 5 cm has the largest volume.

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If P is the orthocenter of △ABC, AB = 13, BF = 9,and FC = 5.6, find each measure & the perimeter of triangle ABC.
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Perimeter = 38.6

Step-by-step explanation:

Given

A\ B = 13

B\ F = 9

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Required

Calculate the perimeter of A B C

To calculate the perimeter of A B C, we sum up the sides of the triangle

i.e.

Perimeter = A B + B\ C + A\ C

AB is given in the question already.

So, we need to calculate B F and F C

To solve for BF, we consider triangle B F C

Using Pythagoras Theorem, we have:

B\ C^2 = B\ F^2 + F\ C^2

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B\ C^2 = 112.36

B\ C^2= \sqrt{112.36

B\ C = 10.6

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To calculate A C, we need to calculate A F, considering triangle B F A

Using Pythagoras Theorem, we have:

A\ B^2 = B\ F^2 + A\ F^2

Substitute values for B F and A B;

13^2 = 9^2 + A\ F^2

169= 81 + A\ F^2

A\ F^2 = 169 - 81

A\ F^2 = 88

A\ F = \sqrt{88

A\ F = 9.4

Since F lies on line A C:

A\ C = A\ F + F\ C

A\ C = 9.4 + 5.6

A\ C = 15.0

Recall that:

Perimeter = A\ B + B\ C + A\ C

Perimeter = 13 + 10.6 + 15.0

Perimeter = 38.6

<em>Hence, the perimeter is 38.6</em>

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