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# Draw a right triangle in which the sides (other than hypotenuse) are of lengths 4 cm and 3 cm. Then construct another triangle whose sides are $\frac{5}{3}$ times the corresponding sides of the given triangle.

Given:

A right triangle in which the sides (other than hypotenuse) are of lengths \( 4 \mathrm{~cm} \) and \( 3 \mathrm{~cm} \).

To do:

We have to draw a right triangle in which the sides (other than hypotenuse) are of lengths \( 4 \mathrm{~cm} \) and \( 3 \mathrm{~cm} \). Then construct another triangle whose sides are \( \frac{5}{3} \) times the corresponding sides of the given triangle.

Solution:

__Steps of construction:__

(i) Draw a line segment $BC = 4\ cm$.

(ii) At $B$, draw perpendicular $BX$ and cut off $BA = 3\ cm$.

(iii) Join $AC$.

$ABC$ is the required triangle.

(iv) Draw a ray $BY$ making an acute angle with $BC$ and cut off five equal parts making $BB_1 = B_1B_2 = B_2B_3 = B_3B_4 = B_4B_5$

(v) Join $B_3$ and $C$.

(vi) From $B_5$, draw $B_5C’$ parallel to $B_3C$ and $C’A’$ parallel to $CA$.

$A’BC’$ is the required triangle.

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