Given that wa = 5x - 8 and wc = 3x + 2, find wb.

Solution:

Given,WA= 5x - 8

WC = 3x + 2

We have to find WB.

Consider triangles △AWZ and △CWZ .

ZW is common.

AZ = CZ

∠AZW =∠CZW = 90.

△AWZ≅ △CWZ, using SAS property.

Therefore WA = WC ------------->(1)

Consider triangles △AWY and △BWY. 

YW is common.

AY = BY

∠AYW =∠BYW = 90.

Thus △AWY ≅ △BWY, using SAS property.

Therefore WA = WB ------------->(2)

From (1) and (2) we determine WA = WB = WC

WA = WB ⇒ 5x - 8 = 3x + 2

By grouping,

5x - 3x = 8 + 2

2x = 10

x = 10/2

x = 5

To find WB substitute the value of x in either of the given equations,

WB = 5(5) - 8

= 25 - 8

= 17

(or)

WB = 3(5) + 2

= 15 + 2

= 17

Therefore, WB = 17

Given that wa = 5x - 8 and wc = 3x + 2, find wb.

Summary:

Given that wa = 5x - 8 and wc = 3x + 2, then wb = 17.

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