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nd AB = 25, Find A(□ ABCD)25Fig. 2.34the figure 2.35, A PQR is anuilatral triangle. Point S is ong QR such thatQR.ove that : 9 PS?7 PQ260°S T |
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Answer» please post complete image of the question Let the side length of an equilateral triangle ∆PQR is a and PT be the altitude of ∆PQR as shown in figure.Now, PQ = QR = PR = a We know, in case of equilateral triangle, altitude divide the base in two equal parts. e.g., QT = TR = QR/2 = a/2 Given, QS = QR/3 = a/3 ∴ ST = QT - QS = a/2 - a/3 = a/6 Also PT = √(PQ² - QT²) = √(a² -a²/4) = √3a/2 Now, use Pythagoras theorem for ∆PST PS² = ST² + PT² ⇒PS² = (a/6)² + (√3a/2)² = a²/36 + 3a²/4 = (a² + 27a²)/36 = 28a²/36 = 7a²/9 ⇒9PS² = 7PQ² Hence proved |
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