Answer:
Priya's age = 15
Amirah's age = 19
Shirley's age = 13
Step-by-step explanation:
Let x be the age of Priya.
According to the question,
Amirah's age = x + 4
Shirley's age = x - 2
Their sum is 47.
So,
x + 4 + x + x - 2 = 47
3x + 2 = 47
3x = 47 - 2
3x = 45
x = 45/3
x = 15
So,
Priya's age = 15
Amirah's age = 15 + 4 = 19
Shirley's age = 15 - 2 = 13
The diagonals are:
diagonal₁=2x+3y
diagonal₂=(x+8)+(2y+5)
We have to solve the following system of equations:
2x=3y
(x+8)=(2y+5)
We solve this system by substitution method:
2x=3y ⇒x=3y/2
(3y/2 +8)=2y+5
3y+16=4y+10
-y=-6
y=6
x=3y/2=3*6/2=9
we obtain the measure of the diagonals:
diagonal₁=2x+3y=2*9+3*6=18+18=36
diagonal₂=(x+8)+(2y+5)=(9+8)+(2*6+5)=17+17=34
Answer: The longest diagonal is 36 units.
