Question

The hypotenuse of a right triangle is 17cm long if one of the remaining two sides is 8 cm in length. Find the length of the other side.​

Answer 1

Given :

• The hypotenuse of a right triangle = 17 cm
• The length of other side = 8 cm

To find :

• The length of other side

According to the question,

By using Pythagoras theorem,

• (Hypotenuse)² = (Perpendicular)² + (Base)²

So, we have considered,

• BC as Hypotenuse.
• CA as Perpendicular.
• AB as Base.

➞ (BC)² = (CA)² + (AB)²

➞ Substituting the values,

➞ (17)² = (8)² + (AB)²

➞ 289 = 64 + (AB)²

➞ 289 - 64 = (AB)²

➞ 225 = (AB)²

➞ √225 = AB

➞ 15 = AB

• So,the length of other side is 15 cm.

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Answer 2

$\boxed{\huge{\sf{AnswEr-:}}}$

• $\boxed{\blue{\sf{\star{\:The\:other\:side\:of\:triangle\:is= 15 cm }}}}$

Explanation-:

$\large{\sf{Given-:}}$

• • The hypotenuse of a Right angled triangle is 17 cm .

• •One of the remaining two sides is 8cm.

$\large{\sf{To\:Find-:}}$

• •Length of other side .

$\setlength{\unitlength}{1cm}\begin{picture}(6,5)\linethickness{.4mm}\put(1,1){\line(1,0){4.5}}\put(1,1){\line(0,1){3.5}}\qbezier(1,4.5)(1,4.5)(5.5,1)\put(.3,2.5){\large\bf 8}\put(2.8,.3){\large\bf 15}\put(1.02,1.02){\framebox(0.3,0.3)}\put(.7,4.8){\large\bf A}\put(.8,.3){\large\bf B}\put(5.8,.3){\large\bf C}\qbezier(4.5,1)(4.3,1.25)(4.6,1.7)\end{picture}$

$\large{\sf{Solution-:}}$

• • Let the length of other side of triangle be X cm . ..............(1) .

• •$\large{\star{\sf{By \: Applying \:Pythagoras\:Theorem-:}}}$

$\boxed{\blue{\sf{\star{(Hypotenuse)^{2}= (Side_{1} )^{2}+ (Side_{2} )^{2} }}}}$

Here ,

• • Hypotenuse = 17 cm.
• •Side 1 = 8 cm.
• •Side 2 = ??

$\pink{\sf{\rightarrow{(17)^{2}= (8 )^{2}+ (Side_{2} )^{2}}}}$

$\pink{\sf{\rightarrow{289= 64+ (Side_{2} )^{2}}}}$

$\pink{\sf{\rightarrow{289 - 64=(Side_{2} )^{2}}}}$

$\pink{\sf{\rightarrow{225=(Side_{2} )^{2}}}}$

$\pink{\sf{\rightarrow{\sqrt{225}=(Side_{2} )}}}$

$\pink{\sf{\rightarrow{\sqrt{15 cm }= (Side_{2})}}}$

• $\boxed{\blue{\sf{\star{Hence,\:The\:other\:side\:of\:triangle\:is= 15 cm }}}}$

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$\large{\sf{\star{ More \:To\:Know-:}}}$

• •Pythagoras theorem -: It states that in a right-angled triangle, the square of the hypotenuse side is equal to the sum of squares of the other two sides .

• •$\boxed{\blue{\sf{\star{(Hypotenuse)^{2}= (Side_{1} )^{2}+ (Side_{2} )^{2} }}}}$

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