Answer:
The value of y is 64.
The value of z is 225.
Step-by-step explanation:
Given,
AB = 136
BC = 255
∠B = 90°
We have to find the value of 'y' and 'z'.
Solution,
Let assume D is a point on AC.
Then BD = 120
And also given ∠D = 90°
Now in ΔABD
AB = 136 and BD = 120
∠D = 90°
So according to Pythagoras theorem;
"The square of the hypotenuse is equal to the sum of the squares of the other two sides".
[tex]AB^2=BD^2+AD^2[/tex]
On substituting the values, we get;
[tex]136^2=120^2+y^2\\\\18496=14400+y^2\\\\y^2=18496-14400\\\\y^2=4096[/tex]
Now taking square root on both side, we get;
[tex]\sqrt{y^2} =\sqrt{4096} \\\\y=64[/tex]
Hence the value of y is 64.
Again, in ΔBDC
BC = 255 and BD = 120
∠D = 90°
So according to Pythagoras theorem;
"The square of the hypotenuse is equal to the sum of the squares of the other two sides".
[tex]BC^2=BD^2+DC^2[/tex]
On substituting the values, we get;
[tex]255^2=120^2+z^2\\\\65025=14400+z^2\\\\z^2=65025-14400\\\\z^2=50625[/tex]
Now taking square root on both side, we get;
[tex]\sqrt{z^2}=\sqrt{50625}\\\\z=225[/tex]
Hence the value of z is 225.
