Please Help. MNOP~Qrst with a scale factor of 5:4. MP=85mm. What is the value of QT?
To find the value of QT, we can use the concept of relative lengths and scale factors.
Given that MNOP to Qrst has a scale factor of 5:4, we know that the ratio of the lengths in MNOP to Qrst is 5:4. Since MP corresponds to QT, their lengths will have the same ratio.
Let's set up the proportion:
MP/MNOP = QT/Qrst
Plugging in the given values, we have:
85mm/MNOP = QT/Qrst
Now we can solve for QT. But to do that, we need to find the length of Qrst.
Since the scale factor is 5:4, we know that the length of Qrst will be 4/5 (or 0.8) times the length of MNOP. Hence:
Qrst = 0.8 * MNOP
Given that MP = 85mm, we need to find the length of MNOP:
MNOP = MP * (5/4)
MNOP = 85mm * (5/4)
MNOP = 106.25mm
Now, let's substitute our values back into the initial proportion:
85mm/106.25mm = QT/0.8*106.25mm
To find QT, we can cross-multiply and solve for QT:
85mm * 0.8 * 106.25mm = QT * 106.25mm
68mm * 106.25mm = QT * 106.25mm
Dividing both sides by 106.25mm, we get:
QT = 68mm
Therefore, the value of QT is 68mm.
To find the value of QT, we need to understand the concept of scale factor and how it relates to the given measurements.
In this case, the scale factor is given as 5:4, which means that for every 5 units on the larger figure (MNOP), there are 4 corresponding units on the smaller figure (Qrst).
We are given the length of MP as 85mm, and we need to find the length of QT.
Step 1: Set up a proportion using the scale factor:
Let x be the length of QT.
So, we can set up the following proportion:
\( \frac{MN}{Qr} = \frac{5}{4} \)
Step 2: Substitute the given values:
Since we have MP = 85mm, we can find MQ by subtracting the length of MP from the length of MN:
MQ = MN - MP
MQ = 5x - 85
Step 3: Solve the proportion:
Using the proportion from Step 1, we can cross-multiply:
\( 4 \times MQ = 5 \times Qr \)
\(4(5x - 85) = 5x \)
Now, let's solve for x:
\(20x - 340 = 5x \)
\(20x - 5x = 340 \)
\(15x = 340 \)
Divide both sides by 15:
\( x = \frac{340}{15} \)
\( x = 22.67 \)
So, the value of QT is approximately 22.67 mm.
MnoP~QrsT
So MP is the corresponding side of QT.
If the scale factor between the two figures is 5:4, the sides are in the same ratio as well.