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Construct a right triangle whose base is $ 12 \mathrm{~cm} $ and sum of its hypotenuse and other side is $ 18 \mathrm{~cm} $.
Given:
Base $=12\ cm$ and the sum of the hypotenuse and another side $=18\ cm$.
To do:
We have to construct the right triangle with the given measurements.
Solution:
Steps of construction:
(i) Let us draw the base $BC$ of length $12\ cm$.
(ii) Now, construct an angle $XBC$ such that $\angle XBC=90^o$ from point B.
(iii) Now, by taking the measure $18\ cm$ with the compasses let us draw an arc from point $B$ on the ray $BX$ and mark the point of intersection of the ray with the arc as $D$.
(iv) Let us now join $DC$. Now, draw a perpendicular bisector of the line $CD$ and mark the point of intersection of the bisector with the ray $BX$ as point $A$.
(v) Then join $AC$. Therefore the required right-angled triangle is formed.
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