If three quantities are in continued proportion; show that the ratio of the first to third is duplicate ratio of first to the second.
Ratio Proportion
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Question

If three quantities are in continued proportion; show that the ratio of the first to third is duplicate ratio of first to the second.

KnowledgeBoat · Accepted Answer

Let x, y and z be in continued proportion. ∴ x : y = y : z To prove : Substituting y² = xz in R.H.S. of above equation we get, = L.H.S. Hence, proved that ratio of the first to third is duplicate ratio of first to the second.

Mathematics

If three quantities are in continued proportion; show that the ratio of the first to third is duplicate ratio of first to the second.

Ratio Proportion

Related Questions

If y is the mean proportional between x and z; show that xy + yz is the mean proportional between x² + y² and y² + z².

If q is the mean proportional between p and r, show that :
pqr(p + q + r)³ = (pq + qr + pr)³.

If p : q = r : s; then show that:
mp + nq : q = mr + ns : s

Mathematics

If three quantities are in continued proportion; show that the ratio of the first to third is duplicate ratio of first to the second.

Ratio Proportion

Related Questions

If y is the mean proportional between x and z; show that xy + yz is the mean proportional between x2 + y2 and y2 + z2.

If q is the mean proportional between p and r, show that :pqr(p + q + r)3 = (pq + qr + pr)3.

If p : q = r : s; then show that:mp + nq : q = mr + ns : s

If y is the mean proportional between x and z; show that xy + yz is the mean proportional between x² + y² and y² + z².

If q is the mean proportional between p and r, show that :
pqr(p + q + r)³ = (pq + qr + pr)³.

If p : q = r : s; then show that:
mp + nq : q = mr + ns : s