RT tegak lurus dengan TQ dan PS Tegak lurus QR. Panjang TP=6cm,PQ=18cm,TR=9cm dan QR=24cm. Tentukan luas segitiga PQR
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Pertanyaan
RT tegak lurus dengan TQ dan PS Tegak lurus QR. Panjang TP=6cm,PQ=18cm,TR=9cm dan QR=24cm. Tentukan luas segitiga PQR
1 Jawaban
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1. Jawaban Milieth
PR=√TP²+TR²
=√(6cm)²+(9cm)²
=√36cm²+81cm²
=√117cm²
=3√13cm
s=1/2K
=1/2(PQ+QR+PR)
=1/2(18cm+24cm+3√13cm)
=1/2(42cm+3√13cm)
=21cm+3√13cm/2
=21cm+1,5√13cm
L PQR=√s(s-a)(s-b)(s-c)
=√(21cm+1,5√13cm)((21cm+1,5√13cm)-18cm)((21cm+1,5√13cm)-24cm)((21cm+1,5√13cm)-3√13cm)
=√(21cm+1,5√13cm)(3cm+1,5√13cm)(-3cm+1,5√13cm)(21cm-1,5cm√13cm)
=√(63cm²+31,5√13cm²+4,5√13cm²+2,25cm√169cm²)(-63cm²+4,5√13cm²+31,5√13cm²-2,25cm√169cm²)
=√(63cm²+36√13cm²+29,25cm²)(-63cm²+36√13cm²-29,25cm²)
=√(-3969cm⁴+2268√13cm⁴-1842,75cm⁴-2268√13cm⁴+1296√169cm⁴-1053√13cm⁴-1842,75cm⁴+1053√13cm⁴-855,5625cm⁴)
=√8.510,0625cm⁴+1.296√169cm⁴
=√8.510,0625cm⁴+1.6848cm⁴
=√25.358,0625cm⁴
=159,24cm²