Question

13. HP Reason Inductively identify two additional values for x and y in a direct variation relationship where y = 11 when x = 18. y = and X= y = 14. MP Persevere with Problems Find y when x= 14 if y varies directly with x?, and y = 72 when x = 6. 15. MP Model with Mathematics Tom is drawing rectangles in which the length varies directly with the width. One of his rectangles has a width of 2 centimeters and a length of 3.6 centimeters. Draw and label a rectangle with a width of 3.5 centimeters that could be one of Tom's rectangles. Then find the perimeter.

Answer 1

15.

Tom draws rectangles whose length are width are related. Lets say that given one of the sides, by multiplying this numer by a constant, we should get the other one. Let k be this constant . So, given a width of 2, we have a length of 3.6. An equation would be

`2\cdot k\text{ = 3.6 }`

So if we want to find the value of k, then

`k\text{ = }(3.6)/(2)\text{ = 1.8}`

So, by knowing the width, we multiply this number by 1.8 to get the length. So for a rectangle of a with of 3.5, we get

`3.5\cdot\text{ 1.8 = 6.3}`

So the length of the rectangle should be 6.3