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what are the values of x and y?

a) x= 136/15, y= 17/15
b) x= 64/15, y= 17/15
c) x= 8/15, y= 136/15
d) x= 64/15, y= 136/15

what are the values of x and y a x 13615 y 1715 b x 6415 y 1715 c x 815 y 13615 d x 6415 y 13615 class=

Respuesta :

In the given figure, we have two right angled triangles:
1) Triangle ABC
2) Triangle CDB

Using pythagorean theorem, we can write equations for both triangles.

For triangle ABC:

[tex] (15+x)^{2}= 17^{2}+ y^{2} [/tex]

For triangle CDB:

[tex] y^{2}= 8^{2}+ x^{2} [/tex]

Using the value of y² in the first equation, we get:

[tex] (15+x)^{2}= 289 + 64 + x^{2} \\ \\ 225+30x+ x^{2} =353 + x^{2} \\ \\ 30x=128 \\ \\ x= \frac{128}{30} \\ \\ x= \frac{64}{15} [/tex]

[tex]y^{2}= 8^{2}+ x^{2} \\ \\ y^{2}=64+ ( \frac{64}{15} )^{2} \\ \\ y^{2}= \frac{18496}{25} \\ \\ y= \frac{136}{15} [/tex]

Thus the d option gives the correct values of x and y 

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