Problem #4

In the figure below, PQRS is rectangle. What is value of $latex a + b + c $ ?

Solusi

Berdasarkan kesebangunan segitiga-segitiga dan teorema Phytagoras, diperoleh:

$latex a^2 = 9 \cdot (9 + 16) $

$latex a^2 = 225 $

$latex a = 15 $

$latex b^2 = 9 \times 16 = 144 $

$latex b = 12 $

$latex c^2 = 16 \cdot (9 + 16) $

$latex c^2 = 400 $

$latex c = 20 $

Sehingga, $latex a + b + c = … $

2 pemikiran pada “Problem #4”

  1. Bisa juga dengan menyelesaikan sistem persamaan berikut:
    $latex a^2 + c^2 = (9 + 16)^2 $ pers i
    $latex b^2 + 9^2 = a^2 $ pers ii
    $latex b^2 + 16^2 = c^2 $ pers iii

    Balas
  2. pers ii dan pers iii
    $latex a^2 + c^2 = 2b^2 + 9^2 + 16^2 $ pers iv

    pers i dan pers iv
    $latex 2b^2 + 9^2 + 16^2 = (9 + 16)^2 $ pers v

    $latex 2b^2 + 9^2 + 16^2 = 9^2 + 2 \ldot 9 \ldot 16 + 16^2 $
    dst

    Balas

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