Odpowiedź:
zad 2
a - bok kwadratu = 18 cm
P₁ - pole trójkąta ADE = 1/2 * a * x = 1/2 * 18 cm * x = 9x cm²
P₂ - pole trapezu = 1/2 * (a + a - x) * a = 1/2 * (2a - x) * a = 1/2 * (2a² - ax) =
= 1/2 * (2 * 18²- 18x) cm²= 1/2 * (2 * 324 - 18x) cm² = 1/2(648 - 18x) =
= (324 - 9x) cm²
324 - 9x = 6 * 9x = 54x
324= 54x + 9x = 63x
63x = 324
x = 324 : 63 = 324/63 cm = 5 9/63 cm = 5 1/7 cm
zad 3
P₁ - pole kwadratu= 40 * 40= 1600 [j²]
P₂- pole trapezu = 1/2* (a + 40) * 40 = (1/2a + 20) * 40 = 20a + 800 [j²]
[j] - znaczy właściwa jednostka
P₁ + 300 = P₂
1600 + 300 = 20a + 800
1900 =20a + 800
2a = 1900 - 800 = 1100
a = 1100 : 2 = 550[j]
