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Question: The longer leg of right angle triangle is 2 more than the shorter leg, and the hypotenuse is 2 less than twice the shorter leg. find the sides of the triangle. Solution:   Let x be the shorter leg longer leg=x+2 hypotenuse=2x-2 apply Pythagoras theorem a 2 +b 2 =c 2 x^2+(x+2)^2=(2x-2)^2 x^2+x^2+4+4x=4x^2+4-8x 2x^2+4x=4x^2-8x 2x^2-12x=0 x^2-6x=0 x(x-6)=0 x=0 or x-6=0 x=6 shorter leg x+2=8 Longer leg 2x-2=10 hypotenuse Check: 6^2+8^2=10^2 36+64=100 ---------------------------------------------------------------------------------------------------------------------------------- Question: The diagonal of a rectangle is 3 less than 4 times the width  of the rectangle. The length of the rectangle is 1 less than the diagonal. Find the length of the diagonal of the rectangle. Solution: Let width of the rectangle=x diagonal of the rectangle=4x-3 Length of rectangle =  (4x-3)-1=4x-4 Leng...

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Question: The base of a triangle is 3 more than twice the  height. If the area of triangle is 10 square centimeters, find the dimension of the triangle? Solution:  Let x be the height of triangle. then the base of triangle is 2x+3. Given Area of triangle =10 sq cm Therefore Area of triangle A=1/2 base*height 10=1/2(2x+3)*x 20=(2x+3)*x 20=2x^2+3x 2x^2+3x-20=0 2x^2+8x-5x-20=0 2x(x+4)-5(x+4)=0 (2x-5)(x+4)=0 Ignore x+4=0 x=-4 Consider 2x-5=0 x=5/2  cm height of triangle base= 2x+3=2*5/2+3=8 cm base of the triangle. Verification: A=(1/2)*(5/2)*8=10 ------------------------------------------------------------------------------------------------------------ Question: A rectangular box with height 3 cm has a volume  of 24 cubic cms. The length of box is 2 more than the width, find the dimensions and volume of the box? Solution: Let x be the width of rectangular box. then the length of rectangular box is x+2. Given height =3 cm and Volu...

Question: Two bicycles start at the same point travelling in the opposite direction. The speed of second bike in miles per hour is 12 less than three times the first. At the end of 6 hours, the bicycles are 144 miles apart. Find the speed of each bicycle. Solution:  Speed *time =Distance 1 st Bicycle x 6 6*x 2 nd Bicycle 3x-12 6 6*(3x-12) Total 144 Then the equation as follows 6*x+6*(3x-12)=144 6x+18x-72=144 24x=216 x=9 miles per hour for 1st bicycle. 3x-12=27-12=15 miles per hour for 2nd Bicycle. ------------------------------------------------------------------------------------------------------------ Question: A Train leaves the Secunderabad station averaging 45mph. A second train leaves the same station two hours later after averaging 60 mph. How long will it take the second train to catch the first train? Solution:   Speed ...