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ivanzaharov [21]
3 years ago
9

Marissa was decorating her room .she arranged 63 same size picture tiles on a wall in the shape of a rectangle.which are possibl

e arrangements of the picture tiles ?
Mathematics
2 answers:
xxMikexx [17]3 years ago
8 0
21 by 3 because 63÷3=21
Mnenie [13.5K]3 years ago
6 0

Answer:

The number of the row could be:  1,3,7,9,21,63

Step-by-step explanation:

There are  63 same size picture tiles

The area of a rectangle is  A = l*w, where:

  • l is the length
  • w is the width

Assume the area of each picture is 1 square unit, so the total are of the wall filled with 63 picture is 63

So to possible arrangements of the picture tiles are factors of 63, we have:

  • 63 = 7 × 9
  • 63 = 3 × 21
  • 63 = 63 × 1

The number of the row could be:  1,3,7,9,21,63

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0.005

Step-by-step explanation:

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John has a job parking cars. He earns a fixed weekly salary of $300 plus a fee of $5 for each car he parks. At what point does J
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Let us assume the number of cars parked after which John will start earning more than his fixed weekly salary = x
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3 years ago
In right △ABC, the altitude CH to the hypotenuse AB intersects angle bisector AL in point D. Find the sides of △ABC if AD = 8 cm
tangare [24]

Answer:

AC=8\sqrt{3}\ cm\\ \\AB=16\sqrt{3}\ cm\\ \\BC=24\ cm

Step-by-step explanation:

Consider right triangle ADH ( it is right triangle, because CH is the altitude). In this triangle, the hypotenuse AD = 8 cm and the leg DH = 4 cm. If the leg is half of the hypotenuse, then the opposite to this leg angle is equal to 30°.

By the Pythagorean theorem,

AD^2=AH^2+DH^2\\ \\8^2=AH^2+4^2\\ \\AH^2=64-16=48\\ \\AH=\sqrt{48}=4\sqrt{3}\ cm

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\dfrac{CA}{CD}=\dfrac{AH}{HD}\\ \\\dfrac{CA}{CD}=\dfrac{4\sqrt{3}}{4}=\sqrt{3}\Rightarrow CA=\sqrt{3}CD

Consider right triangle CAH.By the Pythagorean theorem,

CA^2=CH^2+AH^2\\ \\(\sqrt{3}CD)^2=(CD+4)^2+(4\sqrt{3})^2\\ \\3CD^2=CD^2+8CD+16+48\\ \\2CD^2-8CD-64=0\\ \\CD^2-4CD-32=0\\ \\D=(-4)^2-4\cdot 1\cdot (-32)=16+128=144\\ \\CD_{1,2}=\dfrac{-(-4)\pm\sqrt{144}}{2\cdot 1}=\dfrac{4\pm 12}{2}=-4,\ 8

The length cannot be negative, so CD=8 cm and

CA=\sqrt{3}CD=8\sqrt{3}\ cm

In right triangle ABC, angle B = 90° - 60° = 30°, leg AC is opposite to 30°, and the hypotenuse AB is twice the leg AC. Hence,

AB=2CA=16\sqrt{3}\ cm

By the Pythagorean theorem,

BC^2=AB^2-AC^2\\ \\BC^2=(16\sqrt{3})^2-(8\sqrt{3})^2=256\cdot 3-64\cdot 3=576\\ \\BC=24\ cm

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Step-by-step explanation:

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