12
Объяснение:
Арифметическая прогрессия - это последовательность чисел, каждое из которых меньше предыдущего на число d, называемое разностью арифметической прогрессии.
Обозначим разность за x, тогда
b = a + x
c = b + x = a +2x
S = c + x = a + 3x
По теореме Пифагора a^2 + b^2 = c^2, т. е.
a^2 + (a+x)^2=(a+2x)^2
a^2 + a^2+2ax + x^2 = a^2 + 4ax +4x^2
a^2 - 2ax - 3x^2 = 0
(a - 3x)(a + x) = 0
Т. к. x>0, то x = a/3
S = a*b/2 = a(a+x)/2 = 4a^2/6 = a+3x = 2a, значит, a = 3, x = 3/3 = 1
P = a + b + c = a + a + x + a + 2x = 3a + 3x = 3*3 + 3*1 = 12
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1)Пусть x- сторона 1 и сторона 2, тогда х+2- основа.
По условию задачи периметр равен 20 см причому бічна сторона на 2см менша від основи.
Составом и решим уравнение:
х+х+х+2=20;
3х+2=20;
3х=20-2;
3х=18
х=18:3;
х=6(см)-сторона 1 и сторона 2;
2)20-(6х2)=20-12=8(см)- основание.
ответ: 6 см, 6 см, 8 см
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