Geometry: Similar Triangles and Ratios

If the areas of two similar triangles are 36 cm² and 121 cm², what is the ratio of their corresponding sides?

In triangle ΔPQR, if ray PS bisects ∠QPR with QS = 4.8 cm and SR = 3.6 cm, what is the ratio PQ : PR?

If triangles ΔABC and ΔPQR are similar with sides AB: PQ = 4:5 and A(APQR) = 125 cm², what is the area of triangle AABC?

For two similar triangles with corresponding sides in the ratio 3:5, what is the ratio of their areas?

Given a triangle with a vertical pole of 40 m casting a shadow of 20 m, what will be the length of the shadow of a 50 m tall tower?

If the area of two similar triangles is equal, what can be concluded about their corresponding sides?

In ΔABC where PQ || BC and divides the triangle into two equal areas, how would you express BP/AB?

In the context of similar triangles, if the sides of a smaller triangle are 4 cm, 5 cm, and 6 cm, what is the sum of the sides of the larger triangle if its perimeter is 90 cm?

In a triangle where angle bisector AD divides side BC, what is the ratio of the areas A(ΔABD) to A(ΔACD)?

What is the relationship between the heights of two triangles having equal area when one is scaled by a factor?

If the lengths AB and CD are perpendicular and measured as 3 cm and 4 cm respectively, what is the area of ΔABC?

If ΔABC and ΔPQR are similar and the ratio of their areas is 16:25, what is the ratio of their corresponding sides AB: PQ?

If segments DH and GK are perpendicular to side EF, with respective heights of 12 cm and 20 cm, what can be said about the areas of triangles ADEF and GEF?