GEOMETRY Solve with reasons stated (1 Viewer)

snowflakeptical · Jun 11, 2015

Solve for x, y & z using pythagoras' theorem

ans: x=12, y=6.4, z= 9.6

Squar3root · Jun 11, 2015

to work out x you can use ratio division of line to get:

6/10 = x/8 => x = 12

Squar3root · Jun 11, 2015

then pythogras

(y + z)^2 = (12+8)^2 - 12^2

y + z = 12

InteGrand · Jun 11, 2015

snowflakeptical said:
Solve for x, y & z using pythagoras' theorem

ans: x=12, y=6.4, z= 9.6

$$\frac{GJ}{MJ}=\frac{HK}{MK}$ (corresponding intercepts of intersecting transversals are in equal ratio)$

$$\Rightarrow \frac{x}{8}=\frac{6}{4}\Rightarrow x=12$.$

$By similar reasoning, $\frac{y}{z}=\frac{6}{4}\Rightarrow y = \frac{3}{2}z\Rightarrow GL = y+z = \frac{5}{2}z$.$

$Now, by Pythagoras' theorem in right-angled triangle $GLM$, we have $GL=\sqrt{GM^2 - LM^2}$$

$\Rightarrow \frac{5}{2}z=\sqrt{20^2 - 12^2}$, since $GM = x+8 = 20$

$\Rightarrow \frac{5}{2}z=16$

$\Rightarrow z=6.4.$

$Then $y=\frac{3}{2}z = \frac{3}{2}\times 6.4 = 9.6$.$

snowflakeptical · Jun 11, 2015

Squar3root said:
then pythogras

(y + z)^2 = (12+8)^2 - 12^2

y + z = 12

Oh I get it now!

InteGrand said:
$$\frac{GJ}{MJ}=\frac{HK}{MK}$ (corresponding intercepts of intersecting transversals are in equal ratio)$

$$\Rightarrow \frac{x}{8}=\frac{6}{4}\Rightarrow x=12$.$

$By similar reasoning, $\frac{y}{z}=\frac{6}{4}\Rightarrow y = \frac{3}{2}z\Rightarrow GL = y+z = \frac{5}{2}z$.$

$Now, by Pythagoras' theorem in right-angled triangle $GLM$, we have $GL=\sqrt{GM^2 - LM^2}$$

$\Rightarrow \frac{5}{2}z=\sqrt{20^2 - 12^2}$, since $GM = x+8 = 20$

$\Rightarrow \frac{5}{2}z=16$

$\Rightarrow z=6.4.$

$Then $y=\frac{3}{2}z = \frac{3}{2}\times 6.4 = 9.6$.$

Thanks! You're awesome

Carrotsticks · Jun 11, 2015

Squar3root said:
then pythogras

(y + z)^2 = (12+8)^2 - 12^2

y + z = 12

"pythogras"

Dying

Squar3root · Jun 11, 2015

Carrotsticks said:
"pythogras"

Dying

oops :/

GEOMETRY Solve with reasons stated (1 Viewer)

snowflakeptical

❀

Squar3root

realest nigga

Squar3root

realest nigga

InteGrand

Well-Known Member

snowflakeptical

❀

Carrotsticks

Retired

Squar3root

realest nigga

Users Who Are Viewing This Thread (Users: 0, Guests: 1)

*GEOMETRY* Solve with reasons stated (1 Viewer)

snowflakeptical

❀

Squar3root

realest nigga

Squar3root

realest nigga

InteGrand

Well-Known Member

snowflakeptical

❀

Carrotsticks

Retired

Squar3root

realest nigga

Users Who Are Viewing This Thread (Users: 0, Guests: 1)

GEOMETRY Solve with reasons stated (1 Viewer)