Answer: 11x
---------------------------------------------------
---------------------------------------------------
Explanation:
Let L be the length of rectangle B
There are two copies of L (along the top and bottom of the rectangle). The vertical pairs of sides are both 7x each.
For the triangle, we have three sides of 12x since this is an equilateral triangle. All three sides are congruent for any equilateral triangle.
The perimeter of the triangle is
P = s1+s2+s3
P = 12x+12x+12x
P = 36x
The perimeter of the rectangle is
P = 2*L+2*W
P = 2L+2*7x
P = 2L+14x
Since both perimeters are the same, this means
perimeter of triangle = perimeter of rectangle
36x = 2L+14x
36x-14x = 2L+14x-14x
22x = 2L
2L = 22x
2L/2 = 22x/2
L = 11x
So the length of the rectangle, in terms of x, is 11x. This is the final answer.
Note: if we knew the value of x, then we could find the numeric value of the length for the rectangle. But since we don't know x, we leave it as 11x.
