Solution:
It is given that two triangles Δ ABC and Δ X Y Z are similar by Side -Side - Side(SSS) Similarity theorem.
So, the Statement which is given, that is →→∠B ≅ ∠Y and ∠B ≅ ∠Z, is inadequate for similarity criterion by SSS, as these statement are about angles of Triangles,not sides, which can't be true.
So, if the two triangles are Similar by SSS criterion , then the appropriate mathematical statement must be,
⇒
2x + 2(2x+3) = 360
2x +4x +6 = 360
6x = 360 - 6
6x = 354
x = 354/6
x = 59
answer: x = 59
Explanation:
To find x we need to find the unknown side that connects the two triangles using the Pythagorean theorem:
a² + b² = c² (c is always hypotenuse)
So:
a² + 6² = 9²
a² = 9² - 6²
a² = 81 - 36
a² = 45
a = sqrt45
Now we do the same thing for the other triangle:
x² + 5² = sqrt45²
x² + 25 = 45
x² = 20
x = 2√5 or 4.5...
Add these together.
You get -15y=-45
So y=3
Now plug in to first equation.
8x-8(3)=-16
8x-24=-16
8x=8 so x=1
Check both values in second equation.
-8(1)-7(3)=
-8-21=-29
It works...so x=1, y=3
