In rectangle MNPQ, the ratio of the length of MN to the length of MP is 4:5. a) Does this ratio tell you how long MN is? Explain. b) What if MN is 12 cm long? How long is MP?
a) The ratio of the length of MN to the length of MP tells us the relative lengths between the two sides, but it does not provide the actual length of either side. However, if we know the length of one side, we can use the ratio to find the length of the other side.
b) If MN is 12 cm long, we can set up a proportion based on the given ratio:
MN/MP = 4/5
We can cross-multiply to solve for MP:
5 x MN = 4 x MP
5 x 12 = 4 x MP
60 = 4 x MP
MP = 15 cm
Therefore, if MN is 12 cm long, MP must be 15 cm long in order to maintain the given ratio.
a) The ratio of the length of MN to the length of MP, which is given as 4:5, does not directly tell us the exact length of MN. Instead, it indicates the relationship between the lengths of MN and MP.
To find the actual length of MN, we need additional information. This could be the length of MP, the perimeter of the rectangle, or any other relevant measurements.
b) If we know that MN is 12 cm long, we can use the given ratio to determine the length of MP.
Given: MN = 12 cm
Ratio of MN to MP = 4:5
To find MP, we can set up a proportion using the ratio:
MN/MP = 4/5
Substituting MN = 12 cm, we have:
12/MP = 4/5
Next, we can cross-multiply:
(12)(5) = (4)(MP)
60 = 4MP
Finally, we solve for MP by dividing both sides of the equation by 4:
MP = 60/4 = 15 cm
Therefore, if MN is 12 cm long, MP is 15 cm long based on the given ratio.
a) The ratio of the length of MN to the length of MP being 4:5 does not directly tell us the length of MN. It only tells us the relationship between the lengths of MN and MP.
b) If MN is 12 cm long, we can use the ratio 4:5 to find the length of MP.
Let's set up a proportion using the given ratio:
MN/MP = 4/5
Since we know the length of MN is 12 cm, we can substitute it into the equation:
12/MP = 4/5
To solve for MP, we can cross-multiply and then divide:
(12 * 5) = 4 * MP
60 = 4MP
Finally, divide both sides by 4:
MP = 60/4 = 15 cm
Therefore, if MN is 12 cm long, MP is 15 cm long.