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Construct a right triangle $ABC$ whose base $BC$ is $6\ cm$ and the sum of hypotenuse $AC$ and other side $AB$ is $10\ cm$.
Given:
A right triangle $ABC$ whose base $BC$ is $6\ cm$ and the sum of hypotenuse $AC$ and other side $AB$ is $10\ cm$.
To do:
We have to construct the given triangle.
Solution:
Steps of construction:
(i) Draw a line segment $BC = 6\ cm$
(ii) At $B$, draw a ray $BX$ making an angle of $90^o$ and cut off $BE = 10\ cm$.
(iii) Join $EC$ and draw the perpendicular bisector of $CE$ which intersects $BE$ at $A$.
(iv) Join $AC$.
Therefore,
$\triangle ABC$ is the required triangle.
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