An architect designs a rectangle flower garden such that the width is exactly two thirds of the length. if 310 feet of antique picket fencing are to be used to enclose the garden, find the dimension of the garden.

The dimension of length is 93 feet and dimension of width is 62 feet.

Step-by-step explanation:

Consider the provided information.

Let W represents the width of the rectangle flower garden and L represents the length.

It is given that An architect designs a rectangle flower garden such that the width is exactly two thirds of the length.

This can be written as:

W=2/3L

It is given that the length of fence is 310 feet, that means the perimeter of the rectangle is 310.

Perimeter = 2(L+W)

Substitute the respective values in the above formula.

Substitute the value of L in W=2/3L.

Hence, the dimension of length is 93 feet and dimension of width is 62 feet.

something that characterises a right triangle is the fact that we may use pythagoras' theorem to find any one of its sides given that we have the length of the other two sides. here, we have the length of the hypotenuse, √(87) yd, and one other side, √(23) yd, thus we can easily find the length of the remaining side using pythagoras' theorem as defined below:

c^2 = a^2 + b^2, where c is the length of the hypotenuse, and a and b are the lengths of the other two sides.

thus, given that c = √(87) and a = √(23), we may substitute these into the formula we defined above to get:

c^2 = a^2 + b^2

(√87)^2 = (√23)^2 + b^2 (substitute c = √87 and a = √23 into the equation)

87 = 23 + b^2 (evaluate (√87)^2 = 87 and (√23)^2 = 23 - remember that the square root of a number, squared will equal that very same number)

64 = b^2 (subtract 23 from both sides)

√64 = b (take the square root of both sides)

8 = b (evaluate √64 = 8)

therefor, the length of the unknown leg in the right triangle is 8 yd (first answer).

529 and 531

step-by-step explanation: