Modeling with Quadratic Equations Answers

Which quadratic equation would be used to solve for the unknown dimensions?

Todd and his brother Robert are going to use 512 square feet of their backyard for skateboard ramps. The shape of the backyard is rectangular, with the length twice as long as the width. What are the dimensions of the backyard?

–32–16X 16✔ 32

0 ft 8 ft 16 ft✔ 32 ft

32 ft by 32 ft✔ 64 ft by 16 ft 64 ft by 32 ft 32 ft by 16 ft

He uses the Pythagorean theorem to write an equation to determine the width of the garden.(x)2 + (x + 4)2 = (12)2x2 + x2 + 8x + 16 = 1442x2 + 8x – 128 = 0What are the approximate dimensions of the garden?

The width of the backyard is feet.

Juan wants to change the shape of his vegetable garden from a square to a rectangle, but keep the same area so he can grow the same amount of vegetables. The rectangular garden will have a length that is 2 times the length of the square garden, and the width of the new garden will be 16 feet shorter than the old garden. The square garden is x feet by x feet. What is the quadratic equation that would model this scenario?

After how many seconds does the object hit the ground?

Todd and his brother Robert are going to use 512 square feet of their backyard for skateboard ramps. The shape of the backyard is rectangular, with the length twice as long as the width. What are the dimensions of the backyard?