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.

Answer 1

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.