45.6k views
5 votes
Write an equation to represent the shaded area. Then find the value of x.

Write an equation to represent the shaded area. Then find the value of x.-example-1

2 Answers

8 votes

Final answer:

The equation to represent the shaded area in a rectangle with lengths between x = 2.3 and x = 12.7 is Area = (12.7 - 2.3) \(\times\) h, which simplifies to Area = 10.4 \(\times\) h. To find the value of the shaded area, multiply 10.4 by the value of h.

Step-by-step explanation:

To write an equation representing the shaded area and find the value of x, we look at the properties of geometric shapes. If we are dealing with a rectangle, the area (A) can be calculated using the formula A = length \(\times\) width. In the context of the given problem, if the rectangle is shaded between x = 2.3 and x = 12.7, the length of the rectangle would be represented by the difference of the two x-values, which is 12.7 - 2.3. Assuming the width (or height) of the rectangle is a constant value h, we can represent the area of the shaded region as:

Area = (12.7 - 2.3) \(\times\) h

Calculating this, we get:

Area = 10.4 \(\times\) h

To find the actual shaded area, you need to know the value of h. Once h is known, simply multiply it by 10.4 to get the area.

User Payton Byrd
by
5.6k points
6 votes

Shaded area = (9 + x)(16 + x) = 198

Expand.

x^2 + 25x + 144 = 198

x^2 + 25x - 54 = 0

(x - 2)(x + 27) = 0

x = 2, -27

but x > 0, so

x = 2 cm

User TedTel
by
4.5k points