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In the accompanying diagram, the width of the inner rectangle is represented by 2 - 3 and the length by 2+3. The width of the
outer rectangle is represented by 3 - 4 and the length by 32 +4.
x + 3
x-3
|3x - 4
3x + 4
Part A
Write an expression to represent the area of the larger rectangle.
Part B
Write an expression to represent the area of the smaller rectangle,
x2
Part
Express the area of the region inside the larger rectangle by outside the smaller rectangle as a polynomial in terms of x.

In the accompanying diagram the width of the inner rectangle is represented by 2 3 and the length by 23 The width of the outer rectangle is represented by 3 4 a class=

Respuesta :

abidemiokin
  • The area of the inner triangle is x² - 9
  • The area of the larger triangle is (9x² - 16) sq. units
  • The required polynomial in terms of x is 8x² - 7

The formula for calculating the area of a rectangle is expressed as:

A = LW

  • L is the length
  • W is the width

A) For the inner triangle

Length = x - 3

Width = x + 3

Area of the inner triangle = (x-3)(x+3)

Area of the inner triangle = x²-3x+3x-9

Area of the inner triangle = x² - 9

B) For the larger triangle

Length = 3x-4

Width 3x + 4

A = (3x-4)(3x+4)

A = 9x²+12x-12x-16

A = (9x² - 16) sq. units

Hence the area of the larger triangle is (9x² - 16) sq. units

C) In order to express the area of the region inside the larger rectangle by outside the smaller rectangle as a polynomial in terms of x, we will make the difference in the areas:

P(x) = Area of the larger triangle - Area of the smaller triangle

P(x) = (9x² - 16) - (x² - 9)

P(x) = 9x² - 16 - x² + 9

P(x) = 9x² - x² - 16 + 9

P(x) = 8x² - 7

Hence the required polynomial in terms of x is 8x² - 7

Learn more here: https://brainly.com/question/20968176

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