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3 years ago

ABCD is a rectangle. Find the length of each diagonal. AC = 2(x-3) BD = x+5

Mathematics

2 answers:

alekssr [168]3 years ago

6 0

So this is what I did and I god AC=16 and BD=16

Lapatulllka [165]3 years ago

4 0

AC = 2 (x-3)

BD = x + 5

For this case, the length of the diagonals is the same.

Therefore we have:

AC = BD

Substituting values we have:

2 (x-3) = x + 5

From here, we clear the value of x.

We have then:

2x-6 = x + 5

2x - x = 5 + 6

x = 11

Finally, we substitute the value of x in any of the equations:

11 + 5 = 16

Answer:

the length of each diagonal is:

16 units

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$m_{AB} = \dfrac{A_y-B_y}{A_x-B_x}$

Given this formula, you have the four slopes:

$m_{AB} = \dfrac{A_y-B_y}{A_x-B_x} = \dfrac{-1-2}{-4+1} = \dfrac{-3}{-3} = 1$

$m_{BC} = \dfrac{B_y-C_y}{B_x-C_x} = \dfrac{2-1}{-1-5} = \dfrac{1}{-6} = \dfrac{-1}{6}$

$m_{CD} = \dfrac{C_y-D_y}{C_x-D_x} = \dfrac{1+3}{5-1} = \dfrac{4}{4} = 1$

$m_{DA} = \dfrac{D_y-A_y}{D_x-A_x} = \dfrac{-3+1}{1+4} = \dfrac{-2}{5} = -\dfrac{2}{5}$

Now, two segments are parallel if they have the same slope. So, AB and CD are parallel, because they both have slope 1, but BC and DA are not parallel.

This means that ABCD is not a parallelogram, because in parallelograms the opposite sides are parallel.

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4 years ago

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kodGreya [7K]

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<span>I hope to have helped you ! :)</span>

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irakobra [83]

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3 years ago

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Options B, C, D & E do not comply with the rules for setting up hypotheses

Step-by-step explanation:

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These hypotheses fully complies with our rules.

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H0 should definitely contain the equality claim, although Ha contains it here. Thus, these are not legitimate and don't comply with our rules

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4 years ago

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