In ΔABC, AB is of the length of , and AC is of the length of . The perimeter of ΔABC is 24.
(a) AB = ___units.
(b) AC = ___units.
(c) BC =___ units
To solve this problem, we can use the concept of ratios and proportions. Let's start with the given information:
AB is of the length of BC.
AC is of the length of BC.
The perimeter of ΔABC is 24.
(a) To find the length of AB, let's assume the length of BC is x units.
Since AB is of BC, we can write it as:
AB = x
(b) Similarly, since AC is of BC, we can write it as:
AC = x
(c) Now, we can find BC by using the perimeter of ΔABC. The perimeter of a triangle is the sum of the lengths of all its sides. In this case, it would be AB + BC + AC.
AB + BC + AC = 24
Substituting the values of AB and AC from earlier, we get:
x + x + x = 24
Combining like terms:
3x = 24
Dividing both sides by 3:
x = 8
Now, we can substitute this value of x back into the equations for AB and AC to calculate their lengths.
(a) AB = x = 8 units
(b) AC = x = 8 units
(c) BC = x = 8 units
So, the final answers are:
(a) AB = 8 units
(b) AC = 8 units
(c) BC = 8 units