Help me and show your work.

x = 5/6

Step-by-step explanation:

From the question, we are told that the value of the perimeter equals the value of the area

mathematically, the area of a rectangle is the product of its side lengths

we have this as;

5 * 4x = 20x

The formula for the perimeter is;

P = 2(l + b)

P = 2(5 + 4x)

So we equate this to the area above

20x = 2(5 + 4x)

20x/2 = 5 + 4x

10x = 5 + 4x

10x - 4x = 5

6x = 5

x = 5/6

geometry: triangles

solvers

lessons

answers archive

call the larger triangle abc

then the smaller triangle cde is similar to abc (all angles are equal, aaa).  

ab is the side that is 36, and we wish to find de, the side corresponding to ab

area_cde = area_abc - area_cde --> area_abc / area_cde = 2

let x=length of de

ratio of areas = (ratio of sides)^2

+2+=+%2836%2fx%29%5e2+

+2+=+1296%2fx%5e2+

++x%5e2+=+1296%2f2+=+648+

25.45584