SOLUTION: One side of a rectangular stage is 2 meters longer then the other. If the diagonalis is 10 meters then what are the lenghts of the side?

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Question 171165: One side of a rectangular stage is 2 meters longer then the other. If the diagonalis is 10 meters then what are the lenghts of the side?
Answer by monika_p(71) About Me  (Show Source):
You can put this solution on YOUR website!
a and b are the sides of rectangular, we know that one side is 2 meters longer than the other then b= a+2 and we know that diagonalis d =10m . Now you can use Pythagorean theorem to find a
a%5E2+%2B+%28a%2B2%29%5E2=10%5E2
a%5E2%2B+a%5E2%2B2%2A2%2Aa%2B2%5E2=100
2%2Aa%5E2%2B4%2Aa-96=0
using formula for quadratic equation find a
Aa%5E2%2BB%2Aa%2BC=0
where: A=2, B=4, C=-96
B%5E2-4%2AA%2AC=+16-4%2A2%2A%28-96%29=784
equation has 2 solutions:
a1=%28-B-sqrt%28B%5E2-4%2AA%2AC%29%29%2F%282%2AA%29
a1=%28-4-sqrt%28784%29%29%2F%282%2A2%29
a1=-8 it can not be solution because lenght can not have negative value
a2=%28-B%2Bsqrt%28B%5E2-4%2AA%2AC%29%29%2F%282%2AA%29
a2=%28-4%2Bsqrt%28784%29%29%2F%282%2A2%29
a2=6

If a = 6 meters and b = a+2 , then b= 8meters
Answer: the sides of rectangular stage are 6 & 8 meters long