Question

What is the value of x?

Enter your answer in the box.


_____ units

Answer 1

Answer: The value of x is 28 units.

Explanation:

Since we have given that

DC ║ PA

So, By Basic Proportionate theorem, if a line drawn parallel to the third side and intersect the other two sides, then the other two sides are divided into same ratio.

So, it becomes,

`(RC)/(CA)=(RD)/(DP)\\\\(x)/(10)=(42)/(15)\\\\15* x=10* 42\\\\x=(420)/(15)=28\\\\x=28`

Hence, the value of x is 28 units.

Answer 2

x=28

Explanation:

We can use similar triangles and proportions to solve this problem. Put the side of the small triangle over the same side of the larger triangle.

x 42

---------- = ----------

x+10 42+15

Simplify

x 42

---------- = ----------

x+10 57

Using cross products

57x = 42 (x+10)

Distribute

57x = 42x+420

Subtract 42x from each side

57x-42x = 42x-42x +420

15x = 420

Divide each side by 15

15x/15 = 420/15

x=28