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4 years ago

Why is a rhombus not a rectangle?

Mathematics

1 answer:

alukav5142 [94]4 years ago

4 0

Answer:

A rectangle is a parallelogram with all its interior angles being 90 degrees. A rhombus is a parallelogram with all its sides equal. This means that for a rectangle to be a rhombus, its sides must be equal.

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Find the dimensions of the rectangular corral producing the greatest enclosed area given 320 feet of fencing. (Assume that the l

jenyasd209 [6]

Answer:

The dimensions of the rectangular corral producing the greatest enclosed area is a square of 80 ft x 80 ft

Step-by-step explanation:

Let

x -----> the length of the rectangular corral in feet

y -----> the width of the rectangular corral in feet

we know that

The area of the rectangular corral is equal to

$A=xy$ -----> equation A

The perimeter of the rectangular corral is equal to

$P=2(x+y)$

$P=320\ ft$

$320=2(x+y)$

Simplify

$160=(x+y)$

$y=160-x$ -----> equation B

substitute equation B in equation A

$A=x(160-x)$

$A=-x^2+160x$

This is a vertical parabola open downward

The vertex is a maximum

The x-coordinate of the vertex represent the length for the maximum area

The y-coordinate of the vertex represent the maximum area

Convert the quadratic equation in vertex form

$A=-x^2+160x$

Factor -1

$A=-(x^2-160x)$

Complete the square

$A=-(x^2-160x+80^2)+80^2$

$A=-(x^2-160x+80^2)+6,400$

Rewrite as perfect squares

$A=-(x-80)^2+6,400$

The vertex is the point (80,6,400)

$x=80\ ft$

The maximum area is 6,400 ft^2

<em>Find the value of y</em>

$y=160-x$ ----> $y=160-80=80\ ft$

therefore

The dimensions of the rectangular corral producing the greatest enclosed area is a square of 80 ft x 80 ft

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Answer:

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Answer:

Step-by-step explanation:

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Ha : µ > 34

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Answer:

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