4. Keliling sebuah belah ketupat adalah 60 cm. Jika perbandingan diagonal diagonal 3:4. Hitunglah luas belah ketupat tsb.
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[tex]s = k \div 4 = 60 \div 4 = 15 \\ a = 3x \div 2 = 1.5x \\ b = 4x \div 2 = 2x \\ {a}^{2} + {b}^{2} = {s}^{2} \\ ( {1.5x)}^{2} + ( {2x)}^{2} = {15}^{2} \\ 2.25 {x}^{2} + 4 {x}^{2} = 225 \\ 6.25 {x}^{2} = 225 \\ {x}^{2} = \frac{225}{6.25} = 36 \\ x = \sqrt{36} = 6 \\ d1 = 3x = 3.6 = 18 \\ d2 = 4.6 = 24 \\ \\ luas \: belah \: ketupat \\ \frac{1}{2} \times d1 \times d2 \\ \frac{1}{2} \times 18 \times 24 \\ 216 \: {cm}^{2} [/tex]
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