Question

In a right angled triangle , length of hypotenuse is a cm and length of the one side is b cm . if a -b = 1, find the length of the third side.​

Answer 1

Answer:

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

Let the third side be x cm

$\bf\underline\blue{Using\: Pythagoras\: theorem: -}$

Figure:

$\setlength{\unitlength}{1.5cm}\begin{picture}(6,2)\linethickness{0.5mm}\put(7.7,2.9){\large\sf{A}}\put(7.7,1){\large\sf{B}}\put(10.6,1){\large\sf{C}}\put(8,1){\line(1,0){2.5}}\put(8,1){\line(0,2){1.9}}\qbezier(10.5,1)(10,1.4)(8,2.9)\put(7.2,1.9){\sf{\large{x}}}\put(9,0.7){\sf{\large{b}}}\put(9.4,2){\bf{a}}\put(8.2,1){\line(0,1){0.2}}\put(8,1.2){\line(3,0){0.2}}\put(8.1,1.7){\bf{Venomanish01}}\end{picture}$

$\bf\green{ a^{2} = x^{2} + b^{2} }$

$\bf\green{ x^{2} = a^{2} - b^{2} }$

Putting a = b + 1,

$\bf\green{ x^{2} = (b+1)^{2}-b^{2} }$

$\bf\green{\implies x^{2} = b^{2} +1 +2b-b^{2} }$

$\bf\green{\implies x^{2} = 1 + 2b }$

$\bf\green{\because x = \sqrt{1 + 2b} }$

Hence,

The length of the third side of triangle is $\bf{ \sqrt{1 + 2b} cm}$.

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Additional Information:

What is the Right - Angled Triangle?

A right-angled triangle (also called a right-triangle) is a triangle with a right angle (90°) in it.

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Hope it will be helpful :) ....✍️

Answer 2

Step-by-step explanation:

Using Pythagoras theorem

By Pythagoras theorem

a^2 = (a-2) + ((a-1)/2)^2

a^2 = (a^2-2a+1)/4 + a^2-4a+4 

4a^2 = a^2-2a+1+4(a^2-4a+4)

4a^2 = a^2-2a+1+4a^2-16a+16

a^2 - 18a + 17 =0

(a-17)(a-1) = 0

a = 17

Substitute a = 17 in (2) we get

and length of each side = 17 - 1/2

= 16/2

=8.