A house number is displayed on a plaque in the shape of a regular 7-sided polygon. The area of the plaque is 70 squared inches. The perpendicular distance from a side to the center is 5 inches to the nearest inch. What is the perimeter of the plaque?

The perimeter of the plaque is 28 inches.

Step-by-step explanation:

Given : A house number is displayed on a plaque in the shape of a regular 7-sided polygon. The area of the plaque is 70 squared inches. The perpendicular distance from a side to the center is 5 inches to the nearest inch.

To find : What is the perimeter of the plaque?

Solution :

The 7-sided polygon can be divided into seven triangles whose height, h is equal to the perpendicular distance from each side to the center.

The base of each triangle is equal to the length of a side, s.

The area of each triangle is

The area of the whole polygon is

Now, the perimeter of a regular 7-sided polygon is .

Substitute in area,

We have given,

The perimeter of the plaque is 28 inches.

logv3(x+2)=1

rewrite in exponential form:

logb(x) = y is equal to b^y =x

b = 3, y = 1

now solve for x:

3^1 = x+2)

x = 3-2

x = 1

see the picture for the graph.