Lee's family had a garden in the shape of a right triangle. The total area of the garden is 16 square feet. If they expand the
garden to form a triangle with twice the base and twice the height, by how much will they increase the size of their garden?
16 square feet
32 square feet
48 square feet
64 square feet

The area of the garden is 64 square feet, if the total area of the garden is 16 square feet they expand the garden to form a triangle with the base and twice the height.

Step-by-step explanation:

The given is,

               Total area of the garden is 16 square feet

               If they expand the  garden to form a triangle with twice the base and twice the height

Step:1

              Let, l - Length of the triangle

                    b - Base of the triangle

              Formula for the area of the triangle,

                              ........................(1)

              If the length of triangle is twice

                          - 2 ×

                         w - 2 × w

              For the new area of triangle,

                          ( 2 × ) × ( 2 × w )

                            = 4 ......................(2)

Step:2

            From the equation (1) and (2)

            Twice the length and base of triangle the area will increased 4 times.

                     a = 16 square feet

            Then new area becomes,

                    a = ( 4 × 16 )

                    a = 64 square feet

Result:

           The area of the garden is 64 square feet, if the total area of the garden is 16 square feet they expand the garden to form a triangle with the base and twice the height.

step-by-step explanation:

part a. the differences are decreasing, so we know the sequence is not arithmetic. the ratios are constant (=3/4), so we know the sequence is geometric.

part b. from part a, we know the common ratio is 3/4, so each term is 3/4 of the one before. the initial term is the number of gallons at h=1.

g[h] = (3/4)·g[h-1]

g[1] = 384 . . . . initial value required for a recursive definition

part c. the general formula for a geometric sequence is

a[n] = a[1]·r^(n-1)

we have a[1] = 384, r = 3/4, and the term number given by h. the formula that follows is

g[h] = 384·(3/4)^(h-1)

part d. filling in the value and doing the arithmetic, we have

g[12] = 384·(3/4)^11 ≈ 384·0.042235136 ≈ 16.2183 . . gallons

part e. each gallon is 4 quarts, so

16.2183 gal × 4 qt/gal = 64.8732 qt

step-by-step explanation:

graph using a few selected

x         y

-1       15

0         6

1         2.4

2       0.96