Stosunek długości boków prostokąta o obwodzie 8√2 wynosi 3:2. Oblicz pole tego prostokąta
2a+2b=8√2
a/b=3/2 /*b
a = 3b/2 /*2
2a=3b
3b+2b=8√2
5b=8√2/:5
b=1,6√2
2a=3*1,6√2
2a=4,8√2/:2
a=2,4√2
P=a*b
P=2,4√2*1,6√2
P=7,68cm²
licze na naj ;d
stosunek --> 3:2 czyli3x --> 1 bok 2x ---> 2 bokTeraz obliczamy x: 2 * 3x + 2 * 2x = 8√2 6x + 4x = 8√2 10x = 8√2/:10 x = 0,8√2 1 bok ---> 3x = 3 * 0,8√2 = 2,4√2 2 bok ----> 2x = 2 * 0,8√2 = 1,6√2P = a*bP = 2,4√2 * 1,6√2 P = 7,68[cm²] --> tyle wynosi jego pole
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2a+2b=8√2
a/b=3/2 /*b
a = 3b/2 /*2
2a=3b
2a+2b=8√2
2a=3b
3b+2b=8√2
5b=8√2/:5
b=1,6√2
2a=3b
2a=3*1,6√2
2a=4,8√2/:2
a=2,4√2
P=a*b
P=2,4√2*1,6√2
P=7,68cm²
licze na naj ;d
stosunek --> 3:2 czyli
3x --> 1 bok
2x ---> 2 bok
Teraz obliczamy x:
2 * 3x + 2 * 2x = 8√2
6x + 4x = 8√2
10x = 8√2/:10
x = 0,8√2
1 bok ---> 3x = 3 * 0,8√2 = 2,4√2
2 bok ----> 2x = 2 * 0,8√2 = 1,6√2
P = a*b
P = 2,4√2 * 1,6√2
P = 7,68[cm²] --> tyle wynosi jego pole