The Johnsons want to cover their backyard with new grass. Their backyard is rectangular, with a length of 3x – 5 feet and a width of 4x – 10 feet. However, their rectangular swimming pool, along with its surrounding patio, has dimensions of x + 8 by x – 2 feet. What is the area of the region of the yard that they want to cover with new grass?

Step-by-step explanation:

The formula for determining the area of a rectangle is expressed as

Area = length × width

Their backyard is rectangular, with a length of 3x – 5 feet and a width of 4x – 10 feet. This means that the area of the backyard is

(3x - 5)(4x - 10)

= 12x² - 30x - 20x + 15

= (12x² - 50x + 15) square feet

Their rectangular swimming pool, along with its surrounding patio, has dimensions of x + 8 by x – 2 feet. This means that the area occupied by the swimming pool and its surrounding patio is

(x + 8)(x - 2)

= x² - 2x + 8x - 16

= x² + 6x - 16

Assuming the swimming pool and its surrounding patio will not be covered with new grass, then the area of the region of the yard that they want to cover with new grass is

12x² - 50x + 15 - (x² + 6x - 16)

= 12x² - 50x + 15 - x² - 6x + 16

= 12x² - x² - 50x - 6x + 15 + 16

= 11x² - 56x + 31 square feet

the correct option is 2.

step-by-step explanation:

according to the given information triangle abc is a right angle triangle with right angle at a. segment ab is 5 and segment ac is 7. point d is on segment bc and angles adb and adc are right angles.

it is given that triangles abd, cad, and cba are similar.

two triangles are similar if their corresponding sides are proportional.

in triangle cba, using pythagoras theorem

                      )

triangle abd and cba are similar,

                            (2)

triangle cad and cba are similar,

                      )

using (1), (2) and (3), we get

hence proved.

therefore option 2 is correct.