Question
Find the third proportion to the following :
$(x - y)$ and $m (x - y)$
$(x - y)$ and $m (x - y)$
✓
Answer
Let z be lhe third proportion
$(x - y) : m (x - y) : : m (x - y) : z$
$\Rightarrow (x -y) x z - m(x - y) x m (x - y)$
$\Rightarrow (x - y) z = m^2 (x - y)^2$
$\Rightarrow z = m^2 (x - y)$
The third proportion is $m^2 (x - y) . $
$(x - y) : m (x - y) : : m (x - y) : z$
$\Rightarrow (x -y) x z - m(x - y) x m (x - y)$
$\Rightarrow (x - y) z = m^2 (x - y)^2$
$\Rightarrow z = m^2 (x - y)$
The third proportion is $m^2 (x - y) . $
Need a full question paper?
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.
Explore more
Similar questions
Draw two lines AB, AC so that ∠ BAC = 40°:
(i) Construct the locus of the center of a circle that touches AB and has a radius of 3.5 cm.
(ii) Construct a circle of radius 35 cm, that touches both AB and AC, and whose center lies within the ∠ BAC.
(i) Construct the locus of the center of a circle that touches AB and has a radius of 3.5 cm.
(ii) Construct a circle of radius 35 cm, that touches both AB and AC, and whose center lies within the ∠ BAC.
A part of ₹ $3,020$ is invested in $6 \% $ ₹ $100$ shares at ₹ $97$ and the rest in $12 \% $ ₹ $100$ shares at ₹ $ 108$. If both bring the same dividend, find the sum invested in the shares selling (i) at discount (ii) above par (iii) the total dividend.
→In the following diagram a rectangular platform with a semi-circular end on one side is $22$ metreslong from one end to the other end. If the length of the half circumference is $11$ metres. Find thecost of constructing the platform, $1.5$ metres high at the rate of Rs. $4$ per cubic metres.
→In the figure, $O$ is the centre of the circle and the length of arc $AB$ is twice the length of arc $BC.$ If angle $AOB = 108^\circ$ find $: \angle ADB.$
→If $A=\left[\begin{array}{cc}2 & -1 \\ -4 & 5\end{array}\right]$ and $B=\left[\begin{array}{ll}0 & -3\end{array}\right]$ find the matrix $C$ such that $C A=B$
→In the given figure line $APB$ meets the x-axis at point A and y-axis at point B. P is the point $(-4,2)$ and $AP : PB = 1 : 2.$ Find the co-ordinates of $A$ and $B$
→Two squares have sides x cm and $(x + 4) \ cm$. The sum of their area is $656$ sq. cm. Express this as an algebraic equation in x and solve the equation to find the sides of the squares.
→A rectangular garden $10$ m by $16$ m is to be surrounded by a concrete walk of uniform width. Given that the area of the walk is $120$ square metres, assuming the width of the walk to be x, form an equation in x and solve it to find the value of x.
→Construct the more than cumulative frequency table for the given data :
| Marks | 0 - 10 | 10 - 20 | 20 - 30 | 30 - 40 | 40 - 50 | 50 - 60 | 60 - 70 | 70 - 80 |
| Frequency | 3 | 8 | 12 | 14 | 10 | 6 | 5 | 2 |
Evaluate $2\left(\frac{\tan 35^{\circ}}{\cot 55^{\circ}}\right)+\left(\frac{\cot 55^{\circ}}{\tan 35^{\circ}}\right)-3\left(\frac{\sec 40^{\circ}}{\operatorname{cosec} 50^{\circ}}\right)$
→