Afarmer needs to fence in a rectangular plot of land, and he has 200 meters of fence to work with. he is going to construct the plot next to a river, so he will only have to use fence for three sides of the plot. find the dimensions that will allow the farmer to maximize the area of the plot.

the farmer will need to have 2 pieces of 50 m and one of 100m to maximise the area ( Maximum area=5000 m²)

Step-by-step explanation:

if we assume that the southern fence is not required and if we denote a= length of each lateral side and b= length of the front side , we will have:

Area=A= a*b

Total length of fence=L= 2*a+b

therefore

L= 2*a+b → b= L- 2*a

A= a*(L-2*a) = a*L - 2*a²

therefore

A= a*L - 2*a² → 2*a² - a*L + A = 0

a=  [L ± √((-L)²- 4*2*A)]/(2*2) = L/4  ± √(L²- 8*A) /4

a= L/4  ± √(L²- 8*A) /4

when A goes bigger √(L²- 8*A) diminishes,  but since the minimum possible value √(L²- 8*A) is 0 , then A can not go higher than L²- 8*A=0

therefore

L²- 8*A max=0 → A max = L²/ 8 = (200m)²/8= 5000 m²

and since √(L²- 8*A)=0

a=L/4 = 200m/4 = 50 m

b= L- 2*a = 200m - 2* 50m = 100 m

on your paper it doesn't say the answer but the the answer is altitude

step-by-step explanation:

answer: option a.

step-by-step explanation:

you know that the quadrilateral opqr ( a four sided figure) is inscribed in circle. this means that all its vertices are on the circle.

then, by definition, the opposite angles of the quadrilateral are supplementary, this means that the sum of their measures is 180 degrees.

you can observe in the figure that the angles ∠opq   and the angle ∠orq   are opposite, therefore:

then, can be used to d to calculate the measure of ∠opq