7. Kvadrat quyida ko‘rsatilganidek to‘rt sohaga bo‘lingan. A va B nuqtalar kesma orqali tutashtirilgan. W soha yuzining X soha yuziga nisbati 2:1. W soha yuzining Z soha yuziga nisbati 3:4. X sohaning yuzi 24 cm². a) W, X va Y sohalar yuzi nisbatini toping. b) Kvadratning yuzini toping.

a) Yechish:

1. W:X = 2:1 va X = 24 cm², demak W = 2 × 24 = 48 cm².

2. W:Z = 3:4. W = 48 cm² bo‘lgani uchun Z = 48 × 4 ÷ 3 = 64 cm².

3. AB diagonal kvadratni teng yuzli ikki qismga ajratadi. Shuning uchun W + X = Y + Z. Demak, Y = 48 + 24 − 64 = 8 cm².

4. W:X:Y = 48:24:8 = 6:3:1.

b) Yechish: Diagonalning bir tomonidagi yuz W + X = 48 + 24 = 72 cm². Kvadrat yuzasi buning ikki baravariga teng: 72 × 2 = 144 cm².

Javob: a) 6:3:1; b) 144 cm².