Write an expression to represent the perimeter of the figure.

Mathematics

1 answer:

r-ruslan [8.4K]3 years ago

4 0

Answer:

5x + 2y + z

Step-by-step explanation:

The perimeter of a polygon is the sum of the lengths of all the sides of the polygon. This polygons has 8 sides. Their lengths are:

x, x, x, x, x, y, y, z

The perimeter of the polygon is the sum of the lengths shown above.

perimeter = x + x + x + x + x + y + y + z

The expression above can be simplified by combining like terms.

perimeter = 5x + 2y + z

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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

Elan Coil [88]

Answer:

width: 18 in
length: 27 in

Step-by-step explanation:

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

W +9 = L

LW = 486

Substituting gives ...

(W+9)W = 486

W^2 +9W -486 = 0 . . . put in standard form

(W +27)(W -18) = 0 . . . . factor

W = 18 . . . . the positive solution

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

_____

Comment on factoring

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.