Answer: x= 3 y=5
Explanation:
area=x⋅y=15 cm2
x=15y
perimeter=2x+2y=16 cm
Factoring out the 2 from the L.H.S. Then dividing both sides by 2:
2(x+y)=16
2(x+y)2=162
x+y=8
Substituting our value for x into the above equation:
15y+y=8
Multiplying both sides by y
:
y⋅(15y+y)=8y
y2+15=8y
y2−8y+15=0
The equation above is in the form
Ay2+By+C=0,
where A=1,B=−8,and C=15
The solution to the equation is shown below:
y=−B±B2−4AC√2A
Substituting the values for A, B, and C into the above equation:
y=−(−8)±(−8)2−4⋅1⋅15√2⋅1
Evaluating the above expression:
y=5 or y=3
Therefore, when y=5,x=3
and when y=3,x=5