Question

If the hypotenuse of a right angled triangle is 15 cm and one side of it is 6cm less than the hypotenuse, the other side is equal to:
(a) 12 cm
(b) 21 cm
(c) 9 cm
(d) Ambiguous

Answer 1

Hint: Start by drawing the diagram of the situation given in the figure. For the right angled triangle given in the question, the hypotenuse is equal to 15cm, one of the sides is 6cm less than the hypotenuse, i.e., 15-6=9 cm. So, for finding the length of the third side directly use the Pythagoras theorem and solve the equation you get.

Complete step-by-step answer:
Let us start the solution to the above question by drawing the diagram of the situation given in the question.

For the right angled triangle given in the question, the hypotenuse is equal to 15cm, one of the sides is 6cm less than the hypotenuse, i.e., 15-6=9 cm which is shown in the above diagram.
Now we will apply Pythagora's theorem in $\Delta ABC$ .
${{\left( perpendicular \right)}^{2}}+{{\left( base \right)}^{2}}={{\left( hypotenuse \right)}^{2}}$
$\Rightarrow A{{B}^{2}}+{{9}^{2}}={{15}^{2}}$
$\Rightarrow A{{B}^{2}}={{15}^{2}}-{{9}^{2}}$
Now, we know that ${{15}^{2}}=225$ and ${{9}^{2}}=81$ . If we put this in the above equation, we get
$A{{B}^{2}}=225-81$
$\Rightarrow A{{B}^{2}}=144$
Now, we will take root on both sides of the equation. On doing so, we get
$AB=\sqrt{144}=12cm$

So, the correct answer is “Option A”.

Note: In the question, the key is the diagram and the constructions. The other point to remember is that $A{{B}^{2}}=144$ actually implies $AB=\pm \sqrt{144}=\pm 12cm$ , but we have considered only one value because the length of a side cannot be negative, so only positive value can be the side length. The other point is you must remember the squares of the natural numbers till 20, as they are used very often.