Exercise 6.1: Similar Figures

If ΔABC ~ ΔPQR, and AB/PQ = 3/5. If the perimeter of ΔABC is 36 cm, what is the perimeter of ΔPQR?

In ΔABC, D and E are points on AB and AC respectively such that AD = 3 cm, DB = 5 cm, AE = 4.5 cm, and EC = 7.5 cm. If ∠ADE = 50°, and ∠ABC = 70°, what is the measure of ∠BAC?

In ΔABC, P and Q are points on AB and AC respectively. If AP = x, PB = x-2, AQ = x+2, QC = x-1, for what value of x will PQ be parallel to BC?

A girl of height 90 cm is walking away from the base of a lamppost at a speed of 1.2 m/s. If the lamppost is 3.6 m above the ground, find the length of her shadow after 4 seconds.

A ladder 10 m long reaches a window 8 m above the ground. The distance of the foot of the ladder from the base of the wall is 6 m. Which of the following statements is true about the wall and the ground?

Consider two triangles, ΔABC and ΔDEF. If ∠A = 50°, ∠B = 60°, ∠D = 50°, and ∠F = 70°, which similarity criterion would prove ΔABC ~ ΔDEF?

A ladder 15 m long reaches a window 12 m high from the ground on placing it against a wall at a distance 'a' from the wall. Find the distance 'a'.

In a right-angled triangle PQR, right-angled at Q, if QS ⊥ PR, and PQ = 6 cm, QR = 8 cm. What is the ratio of the area of ΔPQS to the area of ΔRQS?

In ΔABC, D and E are points on AB and AC respectively. If AD = 3 cm, DB = 5 cm, AE = 4.5 cm, and EC = 7.5 cm, and ∠A = 60°, what is the measure of ∠AED?

A ladder 15 m long is placed against a wall such that its foot is 9 m away from the wall. If the top of the ladder slips down by 3 m, how much further will its foot slide away from the wall?