find the area of rectangleRSTU if it is similar to rectangleMNPQ and MN is 4 cm. and MQ is 3cm. while RS is 6cm.
The area of two similar figures is proportional to the squares of the their corresponding sides
So the area of MNPQ = 12
then
RSTU/12 = 6^2/4^2
....
let me know what you got.
i worked the equation and got 3/4 = x/6
RSTU/12 = 36/16
RSTU = 36/16(12) = 27
where does your equation 3/4 = x/6 come from?
from the corresponding sides of each rectangle
Ok, let's do it your way
RV/6 = 3/4
RV = 6(3/4) = 9/2
area of RSTU = (9/2)(6) = 27 , like I had
oh... thank you =]
To find the area of rectangle RSTU, you need to know the corresponding sides of rectangle MNPQ. From the given information, you know that MN is 4 cm and MQ is 3 cm.
Since rectangles RSTU and MNPQ are similar, their corresponding sides are proportional. This means that the ratio of the corresponding side lengths in both rectangles will be equal.
First, let's determine the ratio of corresponding sides:
Ratio of MN to RS = MN / RS = 4 cm / 6 cm = 2/3
Now, we need to find the length of ST, which is corresponding to MQ. We can use the ratio we just determined:
ST / MQ = 2/3
Substituting the given value for MQ (3 cm):
ST / 3 cm = 2/3
Cross-multiplying:
ST = (2/3) * 3 cm
ST = 2 cm
Now we have the length of ST, but we also need the width of the rectangle. As rectangles RSTU and MNPQ are similar, their corresponding sides are also proportional. So, the ratio of corresponding side lengths (RT to NP) will be equal to the ratio of their lengths. Let's calculate this ratio:
Ratio of RT to NP = ST / MN = 2 cm / 4 cm = 1/2
Now, let's find the length of RU, which is corresponding to PQ:
RU / NP = 1/2
Substituting the given value for NP (3 cm):
RU / 3 cm = 1/2
Cross-multiplying:
RU = (1/2) * 3 cm
RU = 1.5 cm
Now we have both the length (ST = 2 cm) and the width (RU = 1.5 cm) of the rectangle RSTU. To find the area, simply multiply these two values:
Area of rectangle RSTU = Length * Width = ST * RU = 2 cm * 1.5 cm = 3 cm²
Therefore, the area of rectangle RSTU is 3 square centimeters.