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mel-nik [20]
3 years ago
11

If the length of a rectangular garden is 2 feet less than the length of a house and the width of the garden is 5 feet less than

half the length of the house, what is the expression for the area of the garden? *
Mathematics
1 answer:
Goshia [24]3 years ago
3 0

Answer:

A(h)  =  h²/2 - 6*h + 10

Step-by-step explanation:

The garden is rectangular, and area of a rectangle is:

A(r) = L*w

Where L is the length and w is the width of the rectangle

Now if we call "h" the length of the house, we have the following expressions

L = h - 2  and

w = h/2 - 5

The expression for the area f the ectangle as a function of the length of the house is:

A(h)  =  ( h - 2 )* ( h/2 -5 )

A(h)  = h²/2 - 5*h - h + 10

A(h)  =  h²/2 - 6*h + 10

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The length of a rectangle is nine inches more than its width. Its area is 486 square inches. Find the width and length of the re
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Answer:

  • width: 18 in
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Step-by-step explanation:

The relations between length (L) and width (W) are ...

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Substituting gives ...

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The width of the rectangle is 18 inches; the length is 27 inches.

_____

<em>Comment on factoring</em>

There are a number of ways to solve quadratics. Apart from using a graphing calculator, one of the easiest is factoring. Here, we're looking for factors of -486 that have a sum of 9.

486 = 2 × 3^5, so we might guess that the factors of interest are -2·3² = -18 and 3·3² = 27. These turn out to be correct: -18 +27 = 9; (-18)(27) = -486.

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