The triangles in the image are similar.
solve for x.
a) 7
b) 6
c) 10
d) 5

ANSWER

A)7

EXPLANATION

The given triangles are similar

Hence the corresponding sides are in the same proportion.

Simplify the right hand side:

Cross multiply;

6(3x+4)=5×30

Expand

18x+24=180

18x=150-24

18x=126

geometry: triangles

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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+

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