Question

Perimetrul unui patrulater este de 637 cm.Daca o latura ar fi mai scurta cu 1/13 din ea, a doua cu 3/13,a treia cu 3/13 ,iar a patra cu 5/13 atunci toate laturile vor fi congruente.Lungimile laturilor. URGENT!!!

Answer 1

Laturile: a,b,c,d;
a + b + c + d = 637;

a - a/13 = b - 3b/13 = c -3c/13 = d - 5d/13;
a - a/13 = d - 5d/13; 13a - a = 13d - 5d, 12a = 8d; a = 8d/12;
a = 2d/3;
b - 3b/13 = d - 5d/13; 13b - 3b = 13d - 5d;  10b = 8d;b = 8d/10;
b = 4d/5;
c - 3c/13 = d - 5d/13; 13c - 3c = 13d - 5d; 10c = 8d;
c = 4d/5;
2d/3 + 4d/5 + 4d/5 + d = 637;
2d/3 + 8d/5 + d = 637;
10d + 24d + 15d = 637x15;
49d = 637x15
d = 13x15;
d = 195 cm;
c = 195x4/5;
c = 156 cm;
b = 4x195/4;
b = 156 cm;
a = 2x195/3;
a = 130 cm.