The distance from one corner of a rectangular garden to the other is 13 ft. the length of the garden is 7 ft longer than the width. write a quadratic equation to find the dimension of the garden. solve the equation and find the area of the garden in square feet.

Step-by-step explanation:

Let x represent the shorter dimension in feet. Then the longer one is x+7 and the Pythagorean theorem tells us the relation of these to the diagonal is ...

  x² + (x+7)² = 13²

  2x² +14x + 49 = 169 . . . . eliminate parentheses

  x² +7x -60 = 0 . . . . . subtract 169 and divide by 2

  (x +12)(x -5) = 0 . . . . factor the equation

  x = -12 or +5 . . . . . . . only the positive value of x is useful here.

The short dimension is 5 ft, so the long dimension is 12 ft. The area is their product, 60 ft².

Comment on finding the area

The quadratic equation above can be rearranged and factored as ...

  x(x +7) = 60

Since the dimensions of the garden are x and (x+7), this product is the garden's area. This equation tells us the area is 60. We don't actually have to find the dimensions.

"a" determine whether sage found the correct quotient. show your work

step-by-step explanation:

there are 70 more legs than eyes at the dog show (196 – 126 = 70). dogs have two more legs than eyes, and humans have the same number of legs as eyes. thus 70 is twice the number of dogs at the show, so the number of dogs is half of 70, which is 35. to get the number of humans, subtract 35 from 63: 63 – 35 = 28.

step-by-step explanation: