Triangles ABC and PQR are similar with m angle A = m angle P and m angle B = m angle Q. If AB, BC, and AC are 3, 4, and 5 ft long respectively and QR is 10 ft, find PQ.
AB/PQ = BC/QR,
3/PQ = 4/10,
4PQ = 30,
PQ = 7.5t.
To find the length of PQ, we can use the concept of similarity of triangles.
Given that triangles ABC and PQR are similar, we know that their corresponding angles are equal. It is given that angle A is equal to angle P and angle B is equal to angle Q.
Using this information, we can deduce that the triangles ABC and PQR have a proportional relationship between their corresponding sides.
Let's determine the ratio between the sides of the two triangles:
Side AB in triangle ABC corresponds to side PQ in triangle PQR.
Side BC in triangle ABC corresponds to side QR in triangle PQR.
Side AC in triangle ABC corresponds to side PR in triangle PQR.
In triangle ABC, AB = 3 ft, BC = 4 ft, and AC = 5 ft.
In triangle PQR, QR = 10 ft.
We can set up the proportion:
AB/PQ = BC/QR = AC/PR
Substituting the known values, we get:
3/PQ = 4/10 = 5/PR
To find PQ, we can cross-multiply and solve for it:
10 * 3 = 4 * PQ
30 = 4 * PQ
PQ = 30/4 = 7.5 ft
Therefore, the length of PQ is 7.5 ft.