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中二數學難題煩請幫忙
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發問:
PQR is a trianlge where PQ=5.3cm and QR=7cm. S is a point on PR such that PS=2.8cn and QS=4.5cm. Find the perimeter and the area of △PQR. 更新: 三角形PQR中，PQ=5.3cm,QR=7cm.S是PR上的一點，PS=2.8cm,QS=4.5cm. 求三角形PQR的周長和面積。
最佳解答:
step 1: prove angle PSQ = 90? √2.8^2 + 4.5^2 = 5.3 L.H.S. = √2.8^2 + 4.5^2 = √7.84+20.25 = √28.09 = 5.3 L.H.S. = R.H.S. by Converse of Pyth. theorem angle PSQ = 90? In trianlge PSQ, RS^2 + SQ^2 = RQ^2 (Pyth. thm) RS^2 + (4.5)^2 = 7^2 RS^2 = 49-20.25 RS = 5.4(corr. to 1 d.p.) The perimeter of trianlge PQR = (5.4+2.8+5.3+7)cm = 20.5cm The area of trianlge PQR = [ 4.5(2.8+5.4) /2 ]cm^2 = [4.5(8.2) /2]cm^2 = 18.45cm^2 Is it correct?
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