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3 years ago

PLEASE HELP The area of a square is 8km. Find its perimeter.

Mathematics

1 answer:

Sidana [21]3 years ago

6 0

Answer:

$area = 8k {m}^{2} \\ l = \sqrt{8} \\ = \sqrt{2 \times 4 } = \sqrt{2} \sqrt{4} \\ l = 2 \sqrt{2} km \\ perimeter = 4 \times l \\ = 4 \times 2 \sqrt{2} \\ = 8 \sqrt{2} km$

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Dima020 [189]

Let $f(x,y,z)=x+y+z-8e^{xyz}$ . The tangent plane to the surface at (0, 0, 8) is

$\nabla f(0,0,8)\cdot(x,y,z-8)=0$

The gradient is

$\nabla f(x,y,z)=\left(1-8yze^{xyz},1-8xze^{xyz},1-8xye^{xyz}\right)$

so the tangent plane's equation is

$(1,1,1)\cdot(x,y,z-8)=0\implies x+y+(z-8)=0\implies x+y+z=8$

The normal vector to the plane at (0, 0, 8) is the same as the gradient of the surface at this point, (1, 1, 1). We can get all points along the line containing this vector by scaling the vector by $t$ , then ensure it passes through (0, 0, 8) by translating the line so that it does. Then the line has parametric equation

$(1,1,1)t+(0,0,8)=(t,t,t+8)$

or $x(t)=t$ , $y(t)=t$ , and $z(t)=t+8$ .

(See the attached plot; the given surface is orange, (0, 0, 8) is the black point, the tangent plane is blue, and the red line is the normal at this point)

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3 years ago

What method do i use to solve this?

skelet666 [1.2K]

Answer: x=20
all angles in the triangle are 180 degree, so:
2x+3x+4x=180
9x=180
divide both sides by 9
x= 20

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