Question

May somebody help me please and thank you.

Answer 1

See below

Explanation:

Eleven

Remark

When you join the midpoints of two sides of a triangle, two properties are true.

1. The Line segment you have drawn is parallel to the third side.
2. 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