<span>The width is 6 inches and the length is 26 inches.
Explanation:
L=4w+2, since the length is 2 more than 4 times the width.
The perimeter is given by P=2L+2w; using our equation for L, we have
P=2(4w+2)+2w.
Using the distributive property, we have
P=2*4w+2*2+2w
P=8w+4+2w.
Combining like terms, we have P=10w+4.
We know the perimeter is 64, so we have
64=10w+4.
Subtract 4 from both sides:
64-4=10w+4-4
60=10w.
Divide both sides by 10:
60/10 = 10w/10
6=w.
Substitute this into the equation for length: L=4*6+2=24+2=26</span>
Answer:
Below in bold.
Step-by-step explanation:
If the 3 points are on the circle with the given center then the distance from each point to the center will all be equal. This distance will be the radius of the circle.
Distance of P (2, 5) from the center (4, 2)
= √( (5-2)^2 + (2-4)^2)
= √(9 + 4)
= √13.
For Q (6, -1)this distance is:
= √(6-4)^2 + (-1-2)^2)
= √13.
For R (7, 4) his distance is:
= √(7-4)^2 + (4-2)^2)
= √13
These distances are the same so the points P, Q and R lie on the circle.
The midpoint of PQ
= (2+6)/2 , (5 - 1)/2
= (4, 2).
Which is the center so this verifies the second part.
