Question

Question 3
Construct the following and give justification :

A right triangle when one side is 3.5cm and the sum of other sides and the hypotenuse is 5.5cm.

Answer 1

Let the given right triangle be ABC.
Given BC = 3.5cm
$\angle B={90}^{\circ }$
The sum of other side and Hypotenuse i.e, AB + AC = 5.5cm

Steps to construct $\Delta ABC$
(i) Draw the base BC = 3.5cm
(ii) Make an angle XBC = ${90}^{\circ }$ at the point B of base BC.
(iii) Cut the line segment BD equal to AB + AC i.e., 5.5cm on the ray XB.
(iv) Join DC and make an $\angle DCY$ equal to $\angle BDC$
(v) Let Y intersect BX at A.
Thus, $\Delta ABC$ is the required triangle.

Justification
Base BC and $\angle B$ are drawn as given.
$In\Delta ACD,\angle ACD=\angle ADC$ [by construction]
$\therefore$ AD = AC . . . . (i)
[sides opposite to equals angles are equal]

Now, AB = BD – AD = BD – AC [from Eq.(i)]
$\Rightarrow$ BD = AB + AC
Thus, our construction is justified

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