Question

What is the value of x?

Answer 1

$\huge \bf{ \underline{ Solution :-}}$

Here we are given a figure of an Isosceles Triangle which has two equal sides of 15 units. The 12 units line, bisector of the vertical angle of the triangle is perpendicular to the opposite side.

$\star \sf{ The \: bisector \: of \: the \: vertical \: angles \: of \: an \: isosceles \: triangle} \\ \sf {bisects \: the \: base \: at \: right \: angle.}$

Therefore,

In the right angle,

Let the Base be a

Perpendicular = 12 units

Hypotenuse = 15 units

We know that, according to Pythagoras Theorem,

$\bf \red{ {Hypotenuse}^{2} = {Perpendicular}^{2} + {Base}^{2} }$

$\rightarrow {15}^{2} = {12}^{2} + {a}^{2}$

$\rightarrow {a}^{2} = {15}^{2} - {12}^{2}$

$\rightarrow a = \sqrt{ {15}^{2} - {12}^{2} }$

$\rightarrow a = \sqrt{225 - 144}$

$\rightarrow a = \sqrt{81}$

$\rightarrow a = 9$

As the perpendicular divides the base into 2 equal parts,

$\therefore x = a + a = (9 + 9) = 18 \: units$

$\bf \purple{The \: Value \: of \: x \: is \: 18 \: units.}$