Amn equilateral triangle with the length of its sides given as 4acm,3bcm and (a+b+c)cm. Find a and b and hence find the length of the sides of the triangle.
In an equilateral triangle, all three sides are equal in length. Therefore, we can set up the following equations based on the given information:
4a = 3b = a + b + c
From the first two equations:
4a = 3b
a = (3/4)b
Substitute this into the third equation:
4a = 3b = (3/4)b + b + c
4(3/4)b = 3b = (3/4)b + b + c
3b = 3/4 b + b + c
3 = 7/4 b + c
Now, substitute back into the second equation to solve for a:
3 = 7/4 b + c
3 = 7/4 b + (4/3)*7/4 b
3 = 7/4 b + 7/3 b
3 = 29/12 b
b = 36/29 cm
Now, find a using the equation:
a = (3/4)b
a = (3/4)*(36/29)
a = 9/29 cm
Now that we have a and b, we can find c:
4a = 3b = a + b + c
4(9/29) = 3(36/29) = 9/29 + 36/29 + c
36/29 = 108/29 = 45/29 + c
c = 63/29 cm
Therefore, a = 9/29 cm, b = 36/29 cm, and c = 63/29 cm. The length of the sides of the triangle are 9/29 cm, 36/29 cm, and 63/29 cm.