Given PQR ~ WXY, p = 18cm, w = 30cm and the area of WXY is 100cm2
a) determine the area of
PQR
p/w = 18/30 = 3/5
so area PQR = (3/5)^2 * WXY
To determine the area of triangle PQR, we can use the formula for the area of similar triangles.
Since triangles PQR and WXY are similar, their corresponding sides are proportional.
Let's denote the area of triangle PQR as A_{PQR}. The area of triangle WXY is given as 100 cm².
The ratio of the corresponding side lengths is given by:
PR/PW = QR/QX = RP/RW
In this case, p = 18 cm and w = 30 cm.
We can set up the proportion:
18/30 = QR/QX = RP/RW
Simplifying, we get:
3/5 = QR/QX = RP/RW
Now, we can use the proportion to determine the ratio of the areas:
(A_{PQR})/(100) = (QR/QX)^2 = (RP/RW)^2
Substituting the ratio obtained from the first proportion:
(A_{PQR})/(100) = (3/5)^2 = 9/25
Now, we can solve for the area of triangle PQR:
A_{PQR} = (9/25) * 100 cm²
A_{PQR} = 36 cm²
Therefore, the area of triangle PQR is 36 cm².
To determine the area of ΔPQR, we can use the concept of similarity between triangles.
Given that ΔPQR is similar to ΔWXY, we can use the property that the ratio of areas between two similar triangles is equal to the square of the ratio of their corresponding side lengths.
Let's find the ratio of side lengths between ΔPQR and ΔWXY:
p/w = 18/30 = 3/5
Since the ratio of sides is 3/5, the ratio of areas will be the square of this ratio: (3/5)^2 = 9/25.
Now, we know that the area of ΔWXY is 100 cm^2. Using the ratio of areas, we can find the area of ΔPQR:
Area of ΔPQR = (Area of ΔWXY) * (Ratio of areas)
Area of ΔPQR = 100 cm^2 * (9/25)
Area of ΔPQR = 900/25 cm^2
Area of ΔPQR = 36 cm^2
Therefore, the area of ΔPQR is 36 cm^2.