This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
Haya master, hapa kuna masuluhisho ya maswali yako: 1. Tafuta thamani ya x. Hatua ya 1: Katika mstatili, pande zinazoelekeana ni sawa. Hivyo, urefu wa upande ZY ni sawa na urefu wa upande WX. ZY = WX Hatua ya 2: Badilisha misemo ya aljebra kwa urefu wa pande: x+5 = 2x-2 Hatua ya 3: Kusanya vigezo (x) upande mmoja na nambari upande mwingine: 5+2 = 2x-x 7 = x Thamani ya x ni 7. 2. Tafuta urefu wa ulalo WY. Hatua ya 1: Kwanza, kokotoa urefu wa pande za mstatili kwa kutumia x=7: Urefu wa WX (au ZY): WX = 2x-2 = 2(7)-2 = 14-2 = 12 cm Urefu wa WZ (au XY): WZ = x-2 = 7-2 = 5 cm Hatua ya 2: Katika mstatili, kila pembe ni 90^. Hivyo, pembetatu WXY ni pembetatu ya pembe mraba. Tunaweza kutumia kanuni ya Pythagoras* kupata urefu wa ulalo WY. WY^2 = WX^2 + XY^2 Hatua ya 3: Badilisha urefu wa pande WX na XY (ambayo ni sawa na WZ) kwenye kanuni: WY^2 = (12)^2 + (5)^2 WY^2 = 144 + 25 WY^2 = 169 Hatua ya 4: Tafuta mzizi wa mraba wa pande zote mbili ili kupata urefu wa WY: WY = sqrt(169) WY = 13 cm Urefu wa ulalo WY ni 13 cm. 3 done, 2 left today. You're making progress.