In a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.
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An aeroplane leaves an airport and flies due north at a speed of $1000\ km$ per hour. At the same time, aeroplane leaves the same airport and flies due west at a speed of $1200\ km$ per hour. How far apart will be the two planes after $1\frac{1}{2}\text{hour}?$
D and E are points on the sides AB and AC respectively of a $\triangle\text{ABC}.$ In the following cases, determine whether DE || BC or not.
AD = 5.7cm, DB = 9.5cm, AE = 4.8cm and EC = 8cm.
A vertical pole of lenght 7.5m casts a shadow 5m long on the ground and at the same time a tower casts a shadow 24m long. Find the height of the tower.
The corresponding sides of two similar triangles are in the ratio $2 : 3.$ If the area of the smaller triangle is $48\ cm^2,$ find the area of the larger triangle.
In the given figure, $\angle\text{CAB}=90^\circ$ and $\text{AD}\perp\text{BC}.$ Show that $\triangle\text{BDA}\sim\triangle\text{BAC}.$ If AC = 75cm, AB = 1m, and BC = 1,25m find AD.