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faithcalhoun
17.12.2019 •
Mathematics
The diagonals of quadrilateral qrst intersect at upper p (negative 2 comma 3 ). qrst has vertices at upper q (4 comma 7 )and upper r (negative 3 comma 5 ). what must be the coordinates of upper s and upper t to ensure that qrst is a parallelogram? the coordinates of upper s must be (-8,3)9(-1,1) (negative 1 comma 1 ). (type an ordered pair.)
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Ответ:
Dimensions of the rug = 13 ft × 26 ft
Step-by-step explanation:
Dimensions of the room = 21 ft × 34 ft
Area of the room = 21 × 34 = 714 ft²
Cynthia wants to leave a uniform strip of floor around the rug.
Let the width of the rug = x ft
Then the dimensions of the rug will be = (21- 2x)ft × (34 - 2x)ft
Area of the rug = (21 - 2x)×(34 - 2x) square feet
338 = (21 - 2x)×(34 - 2x)
338 = 714 - 68x - 42x + 4x²
4x² - 110x + 714 - 338 = 0
4x² - 110x + 376 = 0
2x² - 55x + 188 = 0
2x² - 47x - 8x + 188 = 0
x(2x - 47) - 8(x - 47) = 0
(x - 4)(2x - 47) = 0
x = 4,![\frac{47}{2}](/tpl/images/0734/2420/255bb.png)
For x = 23.5 area of the rug will be negative.
Therefore, x = 4 ft will be the width of the rug.
Dimensions of the rug will be 13 ft × 26 ft.