Answer:
G is the smallest
H is the largest
Step-by-step explanation:
Given
[tex]GH = 21[/tex]
[tex]HJ = 24[/tex]
[tex]GJ = 9[/tex]
Required
Which of the statements is true
First, we need to solve for G, H and J as follows:
[tex]G + H = 21[/tex] --- (1)
[tex]H + J = 24[/tex] --- (2)
[tex]G + J = 9[/tex] --- (3)
Make G the subject in (1)
[tex]G = 21 - H[/tex]
Substitute 21 - H for G in (3)
[tex]21 - H + J = 9[/tex]
Collect Like Terms
[tex]-H + J = 9 - 21[/tex]
[tex]-H + J = -12[/tex]
Make J the subject
[tex]J = H - 12[/tex]
Substitute H - 12 for J in (2)
[tex]H + H - 12 = 24[/tex]
[tex]2H - 12 = 24[/tex]
Collect Like Terms
[tex]2H = 24 + 12[/tex]
[tex]2H = 36[/tex]
Solve for H
[tex]H = 18[/tex]
Substitute 18 for H in [tex]J = H - 12[/tex]
[tex]J = 18 - 12[/tex]
[tex]J = 6[/tex]
Substitute 18 for H in [tex]G = 21 - H[/tex]
[tex]G = 21 - 18[/tex]
[tex]G = 3[/tex]
So, we have that:
[tex]G = 3[/tex] [tex]J = 6[/tex] [tex]H = 18[/tex]
Hence, we can conclude that:
G is the smallest
H is the largest
