Answer:
See below
Step-by-step explanation:
Eleven
Remark
When you join the midpoints of two sides of a triangle, two properties are true.
- The Line segment you have drawn is parallel to the third side.
- The Line segment you have drawn is 1/2 the size of the third side.
For this question, the first property is not as important as the second.
it means that DE is 1/2 the size of GJ
Equation
4x + 5 = 1/2 * (3x + 25)
Solution
Multiply both sides by 2
2(4x + 5) = 2*[1/2*(3x + 25) Simplify
2(4x + 5) = 3x + 25 Remove the brackets on the left
8x + 10 = 3x + 25 Subtract 3x from both sides
8x-3x + 10 = 25 Subtract 10 from both sides.
5x = 25 - 10
5x = 15
x = 3 Answer
DE = 4*3 + 5
DE = 17 Answer
Ten
I wasn't quite sure if you wanted this done.
Givens
MP is the perpendicular bisector of NL
That makes the triangle isosceles.
ML = MN
PL = PN
Solution
ML = MN
7x + 9 = 11x -7 Subtract 11x from both sides.
7x - 11x + 9 = 11x-11x-7
-4x + 9 = - 7 Subtract 9 from both sides.
-4x + 9-9 = -7-9 Combine
-4x = - 16 Divide by - 4
-4x/-4 = - 16/-4
x = 4
==============
PL = PN
2y + 2 = 16 Subtract 2
2y + 2-2 = 16-2 Combine
2y = 14 Divide by 2
2y/2 = 14/2 Combine
y = 7
