1 Answer

Alexander Korovin · Answer 1 · 2023-12-23T11:06:35+0000

Question:

Solution:

Consider the following diagram that represents the given problem:

Now, since P is the midpoint of DE, we get the following equation:

$DE\text{ = DP + PE = DP + DP = 2(DP)}$

According to the diagram, this is equivalent to:

$14x-10=DE\text{ = 2(DP) = 2(6x+4)}$

this is equivalent to:

$14x-10\text{ = 2(6x+4)}$

Applying the distributive property, this is equivalent to:

$14x-10\text{ = }12x\text{ + 8}$

putting together similar terms, this is equivalent to:

$14x\text{ - 12x = 8 + 10 }$

this is equivalent to:

$2x\text{ = 18}$

solving for x, we get:

$x\text{ = }(18)/(2)\text{ =9}$

replacing this into the following equation:

$DP\text{ = 6x+4}$

we get:

$DP\text{ = 6x+4 = 6(9)+4 = 54 + 4 = 58}$

so that, we can conclude that the correct answer is:

$DP\text{ = 58}$

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