Question

Suma dlugosci boku i przekatnej kwadratu jest rowna 10 cm.oblicz pole kwadratu.

Answer 1

A - bok kwadratu
d = a*√2 - przekatna kwadratu
a + d = 10 cm
Pkw. = ? - pole kwadratu

1. Obliczam bok kwadratu
a + d = 10 cm
a + a*√2 = 10 cm
a(1 + √2) = 10
a = 10 : (1 + √2)
a = [10 : (1 + √2)]*[ (1 - √2):(1 - √2)] a = [10(1- √2)]:[ 1^2 - (√2)^2]
a = [10(1- √2)]:[ 1 -2]
a = [10(1- √2)]:[ -1]
a = - 10(-√2 +1)
a = -(-10)(√2 -1 )
a = 10(√2 -1)
a = ok. 4,14 cm
2. Obliczam pole kwadratu
P kw. = a^2
Pkw. = [10(√2 -1)]^2
Pkw. = 100*(√2 -1)^2
Pkw. = ok. 17.16 cm^2