An equilateral triangle has sides of length(3k-2)units. a regular pentagon(5 sides) has sides of (2k+0.5)units. if the perimeter of the triangle is twice the perimeter of the pentagon, find the dimensions of each shape.

The length of side of triangle is 5 units and length of side of pentagon is 1.5 units.

SOLUTION:

Given, An equilateral triangle has sides of length units.  

Then, perimeter of the triangle will be

A regular pentagon (5 sides) has sides of units.  

Then, perimeter of the pentagon will be

We have to find the dimensions of each shape . Now, the perimeter of the triangle is twice the perimeter of the pentagon,  

So,

Then, length of side of triangle

Length of side of pentagon

We have to neglect, negative sign as lengths can’t be negative. Even if we change the sign above all conditions are satisfied.

simplifying

5(x + -6) = 2(x + 3)

reorder the terms:

5(-6 + x) = 2(x + 3)

(-6 * 5 + x * 5) = 2(x + 3)

(-30 + 5x) = 2(x + 3)

reorder the terms:

-30 + 5x = 2(3 + x)

-30 + 5x = (3 * 2 + x * 2)

-30 + 5x = (6 + 2x)

solving

-30 + 5x = 6 + 2x

solving for variable 'x'.

move all terms containing x to the left, all other terms to the right.

add '-2x' to each side of the equation.

-30 + 5x + -2x = 6 + 2x + -2x

combine like terms: 5x + -2x = 3x

-30 + 3x = 6 + 2x + -2x

combine like terms: 2x + -2x = 0

-30 + 3x = 6 + 0

-30 + 3x = 6

add '30' to each side of the equation.

-30 + 30 + 3x = 6 + 30

combine like terms: -30 + 30 = 0

0 + 3x = 6 + 30

3x = 6 + 30

combine like terms: 6 + 30 = 36

3x = 36

divide each side by '3'.

x = 12

simplifying

x = 12

this should .

6 and 24

step-by-step explanation:

6 x 4 = 24