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3 years ago

XY = 4x, YZ = 3x, and XZ = 42

Mathematics

1 answer:

grin007 [14]3 years ago

7 0

Answer:

x=6

XY=24 units

YZ=18 units

Step-by-step explanation:

we have that

Y is between X and Z

$XZ=XY+YZ$

substitute the given values and solve for x

$42=4x+3x\\42=7x\\x=6$

therefore

$XY=4x=4(6)=24\ units\\YZ=3x=3(6)=18\ units$

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Answer:

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b. x + 24

c. Length of the tennis court = 78 feet

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Step-by-step explanation:

a. Perimeter of the rectangle = 2(length + width)

So, perimeter of the tennis court = 2[(2x + 6) + x]

= 2(3x + 6)

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Perimeter of the Basketball court = 2[(3x - 14)+( $\frac{1}{2}$ x + 32)]

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b. Perimeter of the Basketball court - perimeter of the tennis court

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= 7x + 36 - 6x - 12

= x + 24

So, perimeter of the basketball court is x + 24 feet greater than that of the tennis court

c. It is given that the width of the tennis court = 36 feet

But, from the figure,

width of the tennis court = x

So, x = 36

Therefore, length of the tennis court = 2x + 6

= 2(36) + 6

= 72 + 6

= 78 feet

Width of the tennis court = x = 36 feet

Length of the basketball court = 3x - 14

= 3(36) - 14

= 108 - 14

= 94 feet

Width of the basketball court = $\frac{1}{2} x+32$

$=\frac{1}{2} (36)+32$

= 18 + 32

= 50 feet

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