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3 years ago

7

Patrick is replacing a door in his house. It has a height of 80 inches and its diagonal is 89 inches. What is the width of the d

oor?
The door is __________ inches wide.

1 answer:

Sedbober [7]3 years ago

6 0

72 I think I hope its right I had to write all over my paper lol

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Answer:

The answer is "12 inches".

Step-by-step explanation:

Please find the image file of the graph.

We know $AE = CF \ and \ EB = FB$ so because the triangle is isosceles.

$EB = 2x, FB = 2x,\ and \ CF = x$ when $AE$ is called by $x$ .

We know that $AE = AD = x$ since E and D are tangent points to a circle.

They have $CD = CF = x$ since D and F are tangent points only to circle.

Thus, if the perimeter is 32, the following is the result:

$\to AE + EB + BF + FC + CD + DA = 32\\\\\to x + 2x + 2x + x + x + x = 32\\\\\to 8x = 32\\\\\to x = 4$

Therefore the length of $BC = BF + FC = 2x + x = 3x = 12\ inches$

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