Question

The legs of an isosceles triangle have the following lengths in cm:

• 3x-24
• 2x + 1
Find the numerical value of the length of a leg.

Answer 1

To determine the length of a leg of the isosceles triangle, set the two leg expressions equal to each other and solve for x, which is found to be 25. Then, substituting x back into the expressions shows that the length of each leg is 51 cm.

Step-by-step explanation:

To find the numerical value of the length of a leg of an isosceles triangle with leg lengths 3x - 24 cm and 2x + 1 cm, we set the two expressions equal to each other, because the legs of an isosceles triangle are congruent:

3x - 24 = 2x + 1

Solving for x:

1. Subtract 2x from both sides: x - 24 = 1
2. Add 24 to both sides: x = 25

Now that we have the value of x, we can substitute it back into either of the original expressions for the legs to find the actual length of a leg:

Using 3x - 24:
3(25) - 24 = 75 - 24 = 51 cm

Alternatively, using 2x + 1:
2(25) + 1 = 50 + 1 = 51 cm

Therefore, the numerical value of the length of a leg is 51 cm.