Claire bought just enough fencing to enclose either a rectangular garden or a triangular garden, as shown. The two gardens have the same perimeter. How many feet of fencing did she buy?

Step-by-step explanation:

Given,

Perimeter of fencing bought by Claire for rectangular garden

= 2(4x - 4 + x - 4)

= 2 ( 5x - 8 )

= 10x - 16

Perimeter of fencing bought by Claire for triangular garden

= (3x - 1) + (3x - 1) + 3x

= 3x + 3x + 3x - 1 - 1

= 9x - 2

Since,

The two gardens have same perimeter,

By the problem,

10x - 16 = 9x - 2

=> 10x - 9x = 16 - 2

=> x = 14

Hence,

Feet of fencing bought by her,

Putting value in any of the perimeters of the gardens,

10x - 16

= 10(14) - 16

= 140 - 16

= 124 feet (Ans)

x = -5

step-by-step explanation: