Question

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

Answer 1

Answer:

Option 4: 45 units is the correct answer

Step-by-step explanation:

Let $P_1$ be the perimeter of Pentagon and

Let P2 be the perimeter of Triangle

So,

$P_1 = 5(\frac{1}{2}x-1)\\P_2 = 3(x-5)$

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,

$P_1 = P_2\\5(\frac{1}{2}x-1) = 3(x-5)\\\frac{5}{2}x-5 = 3x-15\\\frac{5}{2}x-3x = -15+5\\\frac{5x-6x}{2} = -10\\-\frac{x}{2} = -10\\-x = -10 * 2\\-x = -20\\x = 20$

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