Answer:
[tex]x=3.5,y=24[/tex]
Step-by-step explanation:
The smaller triangle joining the midpoints of the bigger right angle triangle will also be a right angle triangle.
Midpoint Theorem-
According to this, the segment joining two sides of a triangle at the midpoints is half the length of the third side.
Applying this,
[tex]\Rightarrow x=\dfrac{1}{2}(4x-7)[/tex]
[tex]\Rightarrow 2x=4x-7[/tex]
[tex]\Rightarrow 4x-2x=7[/tex]
[tex]\Rightarrow 2x=7[/tex]
[tex]\Rightarrow x=\dfrac{7}{2}=3.5[/tex]
So, the hypotenuses of the bigger triangle will be,
[tex]=6(3.5)+4=25[/tex]
Applying the mid point theorem, the hypotenuses of the smaller triangle will be,
[tex]=\dfrac{1}{2}\times 25=12.5[/tex]
Applying Pythagoras theorem in the smaller triangle, the leg will be
[tex]=\sqrt{12.5^2-3.5^2}\\\\=\sqrt{156.25-12.25}\\\\=\sqrt{144}\\\\=12[/tex]
Again applying mid point theorem,
[tex]\Rightarrow y=2\times 12=24[/tex]
