Answer:
b) - 11
Explanation:
The two triangles ΔJKL and ΔGHK are similar since
LK = 2LH
JK = 2JK
(ratios of sides are same)
and the included angle ∠K is common to both triangles
So the sides are in the ratio 2:1 for larger to smaller triangle. Each side of the larger triangle is twice the length of the corresponding side of the smaller triangle
This means the ratio of side JL of the larger triangle ΔJKL must be twice the length of side GH of the smaller triangle ΔGHK
i.e.
JL = 2 x GH
We are given these sides as expressions in x
∴ x + 27 = 2(2x + 30)
x + 27 = 4x + 60
Subtract 4x from both sides:
x - 4x + 27 = 4x - 4x + 60
-3x + 27 = 60
Subtract 27 from both sides-3x = 60 - 27 = 33
==> 1
- 3x = 33
Divide by -3 both sides
-3x/-3 = 33/-3 = -11
x = -11
Answer b)
Do not be confused by the fact that x is negative. Many students get confused because they associate x as a length. x is just a variable used in the equations
The actual lengths will be positive
GH = 8 and JL = 16
You can work it out yourself