I need help please it’s really hard and I don’t understand it

The line segment HI has length 3x - 5, and IJ has length x - 1.

We're told that HJ has length 7x - 27.

The segment HJ is made up by connecting the segments HI and IJ, so the length of HJ is equal to the sum of the lengths of HI and IJ.

This means we have

7x - 27 = (3x - 5) + (x - 1)

Solve for x :

7x - 27 = (3x + x) + (-5 - 1)

7x - 27 = 4x - 6

7x - 4x = 27 - 6

3x = 21

x = 21/3

x = 7

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

27

step-by-step explanation: