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Practice the questions given in the worksheet on mean proportional.
1. Find the mean proportional of the following sets of positive numbers:
(i) x3y, xy3
(ii) (x - y)2, (x + y)3
2. Find the mean proportional of the following:
(i) 9, 16
(ii) 447, 312
(iii) (a + b)(a - b)3, (a + b)3(a - b)
(iv) x24ab, aby2
3. Find the mean proportional between
(i) 5 and 45
(ii) 0.04 and 0.0036
(iii) 0.25 and 6.25
4. Find the third proportional of the following:
(i) 0.5, 0.25
(ii) a2b, ab2
(iii) xy + yx, xy
5. (i) If the mean proportional of a and c is b then prove that a, c, a2 + b2 and b2 + c2 are proportional.
(ii) If b is the mean proportional of a and c, prove that the mean proportional of a2 + b2 and b2 + c2 is ab + bc.
(iii) If b is the mean proportional of a and c, prove that
(ab+bc+caa+b+c)3=abc
Answers for the worksheet on mean proportional are given below.
Answers
1. (i) x2y2
(ii) x2 - y2
2. (i) 12
(ii) 4
(iii) (a2−b2)2
(iv) x2by
3. (i) 15
(ii) 0.012
(iii) 1.25
4. (i) 0.125
(ii) b3
(iii) x3y(x2+y2)
● Ratio and proportion
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