Question

A regular pentagon and an equilateral triangle have the same perimeter...........

(Please don't answer with anything that doesn't relate to it, such as no mimicking please i beg you)
I only have 1 hour before class help please

Answer 1

Option 4: 45 units is the correct answer

Explanation:

Let
`P_1` be the perimeter of Pentagon and

Let P2 be the perimeter of Triangle

So,

`P_1 = 5((1)/(2)x-1)\\P_2 = 3(x-5)`

In order to find the perimeter of each figure we have to put both the expressions equal so that the value of x can be found and then perimeter.

So,

`P_1 = P_2\\5((1)/(2)x-1) = 3(x-5)\\(5)/(2)x-5 = 3x-15\\(5)/(2)x-3x = -15+5\\(5x-6x)/(2) = -10\\-(x)/(2) = -10\\-x = -10 * 2\\-x = -20\\x = 20`

Putting x = 20 in 2nd perimeter

`P_2 = 3(x-5) \\= 3(20-5)\\= 3(15)\\=45`

As both the perimeters are same, the perimeter of pentagon will also be 45 units.

Hence,

Option 4: 45 units is the correct answer