The GCD(a, b) = 6, the LCM(a, b)=180. Find the least possible value of a+b.
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Answer:
Step-by-step explanation:
Note that the entire segment RT is the combined lengths of RS and ST. So:
We know that RT is 108, RS is (9y+5), and ST is (3y+7). Substitute:
On the right, combine like terms:
Add:
Subtract 12 from both sides. The right cancels:
Divide both sides by 12:
So, the value of y is 8.
To find RS and ST, substitute 8 for y. So:
Substitute 8 for y:
Multiply:
Add:
Do the same for ST:
Substitute 8 for y:
Multiply:
Add: