Find the value of x so that the figures have the same perimeters.

Hello from MrBillDoesMath!

x = 4

Discussion:

Perimeter of rectangle:

= (x +13 + 2x) +   (x +13 + 2x)

= 6x + 26

Perimeter of triangle:

(3x + 4) + (2x+5)  + (5x + 1)

The diagram is a bit fuzzy but I think the above numbers are what is shown

= (3x + 2x + 5x) + (4 +5+1)

= 10x + 10

For the figures to have the same perimeter

6x + 26 = 10x + 10 =>           (subtract 6x from both sides)

6x - 6x + 26 = 10x - 6x + 10 =>

26 = 4x + 10 ->                     (subtract 10 from both sides)

26-10 = 4x =>

16 = 4x =>

x = 16/4 = 4

Check for triangle perimeter:  

10x + 10 =

10(4) + 10 =50

Check for rectangle:

6x + 26

6(4) + 26 = 24 + 26 = 50

The number agree.

Thank you,

MrB

you answer is a

step-by-step explanation:

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