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Find the length of AB, if ΔABC ~ ΔRQP and BC = 14 cm, QP = 7 cm and RQ = 5 cm.

Calculate the hypotenuse of an isosceles right-angled triangle where the equal sides are 8√6 cm each.

What is the length of the hypotenuse in an isosceles right-angled triangle if one of its equal sides measures 5√3 cm?

If in triangle ABC, If side AB=6√ 3, AC=12 and BC=6, then angle B equals:

In triangle ABC, DE is drawn parallel to BC, meeting AB at D and AC at E. If AD : DB = 3 : 2 and the area of triangle ADE is 45 cm², find:

In a right-angled triangle, the two perpendicular sides are 9 cm and 12 cm. What is the radius of the incircle of the triangle?

Find the length of AB, if ΔABC ~ ΔRQP and AC = 22.5 cm, RP = 9 cm and RQ = 6 cm.

Two triangles DEF and XYZ are similar to each other. If DE = 5 cm, DF = 7 cm, and XY = 15 cm, then find XZ.

If the side of an equilateral triangle is 12cm, then find the area (in cm ² ) of the triangle (correct to two decimal places).