Book: RS Aggarwal - Mathematics
Chapter: 10. Quadratic Equations
Subject: Maths - Class 10th
Q. No. 71 of Exercise 10E
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71
The hypotenuse of a right – angled triangle is 1 metre less than twice the shortest side. If the third side is 1 metre more than the shortest side, find the sides of the triangle.
Let the shortest side of triangle be xm
According to the question ;
Hypotenuse = 2x – 1 m
Third side = x + 1 m
Applying Pythagoras theorem
(2x – 1)2 = (x + 1)2 + x2
4x2 – 4x + 1 = x2 + 2x + 1 + x2 using (a – b)2 = a2 – 2ab + b2
2 x2 – 6x = 0
2x (x – 3) = 0
x = 0 or x = 3
Length of side cannot be 0 thus the shortest side is 3m
Hypotenuse = 2x – 1 = 6 – 1 = 5m
Third side = x + 1 = 3 + 1 = 4m
Thus the dimensions of triangle are 3m, 4m and 5m.
minutes. If one pipe takes 3 minutes more than the other to fill it, find the time in which each pipe would fill the cistern.
