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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?
a)16 square feet
b)32 square feet
c)48 square feet
d)64 square feet

the size of the garden increases by 48 sq feet

Step-by-step explanation:

In the triangle lets name the base as A and height as B.

Area of the triangle = 1/2 x A x B

the area given of the triangle = 16 square feet

the new dimensions  

A--->2xA

B ---> 2xB

new area = 1/2 x 2x A x 2xB  

                =(1/2 x A x B) x 2 x 2  

since (1/2 x A x B) = 16

new area = 16 x 4 = 64 sq feet

the increase in size = 64 - 16 =  

the size of the garden increases by 48 sq feet

B

Step-by-step explanation:

the formula for the triangle is ( base * height ) / 2

Start out by multiplying the are they have by 2.  ( 16 * 2 = 32 )

Now I know that (8 * 4 ) = 32. And as we know 32 / 2 = 16 ft^2 which is the original area.

Now they want to double their height and base by two.

So we do ( 8 * 2 ) = 16 and ( 4 * 2 ) = 8 and now we calculate the area with our new values.

( 16 * 8 ) = ( 128 / 2 ) = 64 ft ^2.

Our original area was 16 ft^2 and our knew area is 64 ft^2.

We do ( 64 - 16 ) = 48 ft^2

So they increased their garden by 48 ft^2.

answer: 204

step-by-step explanation:

we are told that the revenue is

x⋅(4080−10x)=−10x^2+4080x

this is a quadratic function, so to maximize it we should find the x-value of its vertex. recall that the x-value of the vertex of the parabola ax^2+bx+c is given by the formula −b/2a.

so in this case, we have a=−10 and b=4080, so the x-value of the vertex is

−b/2a= −(4080)/2(−10)=204

first, you divide the triangle in two, tô form a retangle triangle. after, using pythagoream theorem:

18^2 = 14^2 + (x/2)^2

(x^2/4) + 196 = 324

x^2/4 = 324 - 196

x^2/4 = 128

x^2 = 512

x = √512

x = √2^9

x = 16√2 cm

i hope i you.