Minimizing Construction Costs The management of the UNICO department store has decided to enclose a 945 ft2 area outside the building for displaying potted plants and flowers. One side will be formed by the external wall of the store, two sides will be constructed of pine boards, and the fourth side will be made of galvanized steel fencing. If the pine board fencing costs $7/running foot and the steel fencing costs $4/running foot, determine the dimensions of the enclosure that can be erected at minimum cost. (Round your answers to one decimal place.)

Pine board side = 16.4 ft

Steel fencing side = 57.5 ft

Step-by-step explanation:

Let 'B' be the length of each side constructed of pine boards, and 'S' be the length of the side with the steel fencing, the area (A) and cost (C) functions are:

The value of S for which the derivate of the cost function is zero, minimizes cost:

The value of B is:

Pine board side = 16.4 ft

Steel fencing side = 57.5 ft

i think the length is 12 and the width is 17

isocolese triangle

we know that the line connect a and b is the hyptonuse

so first find the hypotonuse length using the distance formula, call the length c

since it is an isocolese triangle, the lengths of the legs are the same

using pythagorean theorem,

in this case, a=b since isocolese triangle so we get

or

we can find c so we can find the distances

we know that if we draw 2 circles, each has center at a and b, and find where they intersect, we can the 2 possible locations for c

if a has center at (xa,ya) and b has center at (xb,yb), then we can solve where

and

intersect to find where they intersect

i'm not going to put an example because i have to go to class. i hope this explanation is enough