What is the smallest perimeter you can make if the area of a rectangle is 24 units^2?
What is the largest perimeter you can make if the area of a rectangle is 24 units^2?
What is the largest perimeter for a rectangle with an area of 100 units^2?

Smallest perimeter = 19.6 units

Largest perimeter for area of 24 u2 = 50 units (assuming smallest side = 1 unit)

Largest perimeter for area of 100 u2 = 202 units (assuming smallest side = 1 unit)

Step-by-step explanation:

The area of a rectangle is:

Area = length * width

If the area is 24 u2, we have that:

length * width = 24 -> length = 24/width

Then the perimeter is:

P = 2*length + 2*width = 48/width + 2*width

To find the smallest perimeter, we can take the derivative and make it equal to zero to find the width that gives the smallest perimeter:

dP/dwidth = -48/width^2 + 2 = 0

width^2 = 48/2 = 24

width = 4.9

so the length is 24/width = 24/4.9 = 4.9

and the perimeter is 2*4.9 + 2*4.9 = 19.6 units

To find the largest perimeter, we need to assume the smallest value that a side can have. Assuming that this value is 1 unit, we have that:

Area = length * 1 = 24

length = 24 units

Perimeter = 2*24 + 2*1 = 50 units

If the area is 100 u2, the largest area, again assuming smallest value for side equal 1 unit, is:

Area = length * 1 = 100

length = 100 units

Perimeter = 2*100 + 2*1 = 202 units

the k side

step-by-step explanation:

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solution:

we have to construct

∠m nt ≅ ∠p qr

the steps to draw this construction are

step 1: use a compass to draw an arc from point q which intersects the side pq at point a and the side qr at point b.

step 2: draw a segment nt and use the same width of the compass to draw an arc from point n which intersects the segment nt at a point x.

step 3:

step 4: join points n and y using a straightedge.

step 3:

option (d).maintaining the same width of the compass as ab, draw an arc from point x such that it intersects the arc drawn from n in a point y.

to draw   congruent angles , 1. width of compasses while drawing two angles should be same i.e from point at which angle has to be drawn, 2.the distance between the two points where the compass intersects the two sides should be same while drawing any two congruent angles.