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
Step 1: Tambua aina ya pembetatu. Kwa kuwa hakuna pembe iliyoonyeshwa, lakini kuna pande tatu zilizopewa, na kwa kawaida maswali kama haya huashiria pembetatu ya pembe mraba ikiwa hakuna taarifa nyingine, tutachukulia kuwa ni pembetatu ya pembe mraba. Upande mrefu zaidi, 28, utakuwa hypotenuse. Step 2: Tumia Theorem ya Pythagoras. Theorem ya Pythagoras inasema kwamba katika pembetatu ya pembe mraba, jumla ya miraba ya pande mbili fupi (miguu) ni sawa na mraba wa upande mrefu (hypotenuse). a^2 + b^2 = c^2 Katika kesi hii, x na 14 ni miguu, na 28 ni hypotenuse. x^2 + 14^2 = 28^2 Step 3: Tafuta thamani ya x^2. Kwanza, hesabu miraba ya nambari zinazojulikana. x^2 + 196 = 784 Toa 196 kutoka pande zote mbili za mlinganyo. x^2 = 784 - 196 x^2 = 588 Step 4: Tafuta thamani ya x. Chukua mzizi wa mraba wa 588. x = sqrt(588) Ili kurahisisha mzizi wa mraba, tafuta vigawo vya mraba kamili vya 588. x = sqrt(4 × 147) x = sqrt(4 × 49 × 3) x = sqrt(4) × sqrt(49) × sqrt(3) x = 2 × 7 × sqrt(3) x = 14sqrt(3) Thamani ya x ni: 14sqrt(3) Tuma swali linalofuata 📸