Question

the hypothesis of right angled is 15 cm one of its lengs is 9 cm what is length of the other side
​

Answer 1

Given:-

• Hypotenuse of right angled triangle is 15 cm.
• One of its length is 9 cm.

To find:-

• Length of other side.

Solution:-

Let,

Perpendicular be 9 cm.

Base or length of other side be x cm.

We know that,

Pythagoras theorem is :

$\boxed{ \sf \bold{ {Base}^{2} + Perpendicular^{2} = {Hypotenuse}^{2} }}$

So,

$\implies \sf {(9)}^{2} + {(x)}^{2} = {(15)}^{2}$

$\implies \sf {(x)}^{2} = {(15)}^{2} - {(9)}^{2}$

$\implies \sf {(x)}^{2} = 225 - 81$

$\implies \sf x = \sqrt{225 - 80}$

$\implies \sf x = \sqrt{144}$

$\implies \boxed{ \sf \bold{x = 12}}$

We have taken length of other side be x.

Therefore,

Length of other side is 12 cm.

Answer 2

Diagram:

$\setlength{\unitlength}{1.5cm}\begin{picture}(0,0)\linethickness{0.7mm}\qbezier(1, 0)(1,0)( 1,3)\qbezier(5,0)(5, 0)(1,3)\qbezier(5,0)(1,0)(1,0)\put(1.4,0){\line(0,3){0.3}}\put(1,0.3){\line(1,0){0.4}}\put(-0.1,1.5){9 cm}\put(0.7,-0.2){ \sf B }\put(3.1,2){15 cm}\put(5.1, - 0.2){ \sf C }\put(0.7,3){ \sf A }\end{picture}$

Answer:

It is Given that, the hypothesis of right angled is 15 cm one of its length is 9 cm.

In right angle triangle ABC,

• AC represents the Hypotenuse of right angle triangle.
• AC = 15 cm
• AB represents one of the side of right angle triangle.
• AB = 9 cm
• BC represents another side of right angle triangle.
• BC = ?

Pythagorean theorem, states that the square of the length of the hypotenuse is equal to the sum of squares of the lengths of other two sides of the right-angled triangle :]

By above definition for right angled triangle ABC,

$=> \sf AC^2 = AB^2 + BC^2$

$=> \sf (15)^2 = (9)^2 + BC^2$

$=> \sf 225= 81 + BC^2$

$=> \sf BC^2 = 225 - 81$

$=> \sf BC^2 = 144$

• Taking square roots on both sides we get :]

$=> \sf BC = \sqrt{144 }$

$=> \textsf{ \textbf{ BC= 12 cm}}$

Therefore, the length of the other side is 12 cm.