Find the mean proportional between the following. a - b a + b and a 2 b 2 a 2 - b 2

If x , y and z are in continued proportion, then y is called the mean proportional. Let the mean proportional between a - b a + b and a 2 b 2 a 2 - b 2 be z . Then, a - b a + b : z : : z : a 2 b 2 a 2 - b 2 ⇒ z 2 = a - b a + b × a 2 b 2 a 2 - b 2 ⇒ z 2 = a - b a + b × a 2 b 2 a - b a + b ⇒ z 2 = a 2 b 2 a + b 2 ⇒ z = a b a + b Hence, the required mean proportional is a b a + b

Find the third proportional to 5 + 2 3 , 37 + 20 3

Given, Two numbers 5 + 2 3 and 37 + 20 3 Let the third proportional to 5 + 2 3 and 15 be x . If x , y and z are in continued proportion, then z is called third proportional. Therefore, 5 + 2 3 : 37 + 20 3 : : 37 + 20 3 : x ⇒ 5 + 2 3 37 + 20 3 = 37 + 20 3 x ⇒ x = 37 + 20 3 2 5 + 2 3 ⇒ x = 37 2 + 20 3 2 + 2 × 37 × 20 3 5 + 2 3 ⇒ x = 1369 + 1200 + 1480 3 5 + 2 3 Rationalize the denominator ⇒ x = 2569 + 1480 3 5 + 2 3 × 5 - 2 3 5 - 2 3 ⇒ x = 2569 + 1480 3 5 - 2 3 5 2 - 2 3 2 ⇒ x = 2569 5 - 2 3 + 1480 3 5 - 2 3 25 - 12 ⇒ x = 12845 - 5138 3 + 7400 3 - 8880 13 ⇒ x = 3965 + 2262 3 13 ⇒ x = 13 305 + 174 3 13 ⇒ x = 305 + 174 3 Hence, the required third proportional is 305 + 174 3 .

Find the third proportional to x y + y x and x y

Given, two numbers x y + y x and x y Let the third proportional to x y + y x and x y be z . If x , y and z are in continued proportion, then z is called third proportional. Therefore, x y + y x : x y : : x y : z ⇒ x y + y x x y = x y z ⇒ z = x y 2 x y + y x ⇒ z = x 2 y 2 x 2 + y 2 x y ⇒ z = x 2 y 2 × x y x 2 + y 2 ⇒ z = x 3 y x 2 + y 2 Hence, the required third proportional is x 3 y x 2 + y 2 .

E M B I B E

All In One ICSE Mathematics Class 10>Algebra>Chapter 6 - Ratio and Proportion>Topic Exercise

Jitender Gupta and Divya Malik Solutions for Exercise 2: Topic Exercise

Author:Jitender Gupta & Divya Malik

Jitender Gupta Mathematics Solutions for Exercise - Jitender Gupta and Divya Malik Solutions for Exercise 2: Topic Exercise

Attempt the practice questions from Exercise 2: Topic Exercise with hints and solutions to strengthen your understanding. All In One ICSE Mathematics Class 10 solutions are prepared by Experienced Embibe Experts.

Questions from Jitender Gupta and Divya Malik Solutions for Exercise 2: Topic Exercise with Hints & Solutions

MEDIUM

10th ICSE

IMPORTANT

All In One ICSE Mathematics Class 10>Chapter 6 - Ratio and Proportion>Topic Exercise>Q 14

Find the mean proportional between the following. $5$ and $80$

MEDIUM

10th ICSE

IMPORTANT

All In One ICSE Mathematics Class 10>Chapter 6 - Ratio and Proportion>Topic Exercise>Q 15

Find the mean proportional between the following.

$\frac{a - b}{a + b}$ and $\frac{a^{2} b^{2}}{a^{2} - b^{2}}$

MEDIUM

10th ICSE

IMPORTANT

All In One ICSE Mathematics Class 10>Chapter 6 - Ratio and Proportion>Topic Exercise>Q 20

Find the third proportional to
$25$ and $15$

HARD

10th ICSE

IMPORTANT

All In One ICSE Mathematics Class 10>Chapter 6 - Ratio and Proportion>Topic Exercise>Q 20

Find the third proportional to

$5 + 2 \sqrt{3}, 37 + 20 \sqrt{3}$

HARD

10th ICSE

IMPORTANT

All In One ICSE Mathematics Class 10>Chapter 6 - Ratio and Proportion>Topic Exercise>Q 21

Find the third proportional to $\frac{x}{y} + \frac{y}{x}$ and $\frac{x}{y}$

MEDIUM

10th ICSE

IMPORTANT

All In One ICSE Mathematics Class 10>Chapter 6 - Ratio and Proportion>Topic Exercise>Q 22

Find the fourth proportional of the following.
$8, 14, 16$

HARD

10th ICSE

IMPORTANT

All In One ICSE Mathematics Class 10>Chapter 6 - Ratio and Proportion>Topic Exercise>Q 33

If $x = \frac{4 \sqrt{6}}{\sqrt{2} + \sqrt{3}}$ , then find the value of $\frac{x + 2 \sqrt{2}}{x - 2 \sqrt{2}} + \frac{x + 2 \sqrt{3}}{x - 2 \sqrt{3}}$ .