In triangle ABC, D and E are midpoints of AB and AC, DE=4x and BC=2x+48. Find BC.
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DE=BC/2
To find the length of BC, we need to find the value of x.
We know that D and E are the midpoints of AB and AC, respectively. This means that DE is parallel to BC, and DE is half the length of BC.
Since DE = 4x and BC = 2x + 48, we can set up an equation based on the relationship between DE and BC:
DE = 1/2 * BC
Substituting the given values:
4x = 1/2 * (2x + 48)
Simplifying the equation:
4x = x + 24
Subtracting x from both sides:
3x = 24
Dividing both sides by 3:
x = 8
Now that we've found the value of x, we can find the length of BC by substituting it back into the equation:
BC = 2x + 48
BC = 2(8) + 48
BC = 16 + 48
BC = 64
Therefore, the length of BC is 64.
To find the length of BC, we need to use the given information about the midpoints and the lengths of DE and BC.
Since D and E are the midpoints of AB and AC respectively, we can apply the midpoint theorem. According to this theorem, the segment connecting the midpoints of two sides of a triangle is parallel to the third side and half its length.
So, DE is parallel to BC and half its length. Therefore, we have the equation:
DE = 1/2 * BC
Now, we substitute the given value of DE as 4x into the equation:
4x = 1/2 * BC
To get the value of BC, we solve this equation:
Multiplying both sides by 2, we get:
8x = BC
Since we also know that BC = 2x + 48, we can set up another equation using this information:
2x + 48 = 8x
Subtracting 2x from both sides, we get:
48 = 6x
Dividing both sides by 6, we get:
x = 8
Finally, we can substitute the value of x back into the equation for BC:
BC = 2x + 48 = 2 * 8 + 48 = 16 + 48 = 64
Therefore, BC = 64.