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kvv77 [185]
3 years ago
12

Consider the diagram below. which of the following represents the values x,y and z?

Mathematics
1 answer:
Gemiola [76]3 years ago
3 0

Answer:

x=4\sqrt{6}\ units

y=4\sqrt{2}\ units

z=4\sqrt{3}\ units

Step-by-step explanation:

The picture of the question in the attached figure

step 1

In the right triangle ABD

Applying the Pythagorean Theorem

x^2=y^2+(12-4)^2

x^2=y^2+64

y^2=x^2-64 ----> equation A

step 2

In the right triangle BDC

Applying the Pythagorean Theorem

z^2=y^2+4^2

z^2=y^2+16

y^2=z^2-16 ----> equation B

step 3

In the right triangle ABC

Applying the Pythagorean Theorem

12^2=x^2+z^2

144=x^2+z^2 ----> equation C

step 4

Equate equation A and equation B

x^2-64=z^2-16

x^2=z^2+48 -----> equation D

step 5

substitute equation D in equation C

144=z^2+48+z^2

solve for z

2z^2=144-48

2z^2=96

z^2=48

z=\sqrt{48}\ units

simplify

z=4\sqrt{3}\ units

Find the value of x

x^2=z^2+48

x^2=48+48=96

x=\sqrt{96}\ units

x=4\sqrt{6}\ units

Find the value of y

y^2=z^2-16

y^2=48-16

y^2=32

y=\sqrt{32}\ units

y=4\sqrt{2}\ units

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<h2><em>Completing The Square</em><em>:</em></h2>

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