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Question

The length of a hypotenuse of a right angle triangle exceeds the length of its base by 2 cm and exceeds twice the length of the altitude by 1 cm. Find the length of each side of the triangle (in cm).

A
6,8,10
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B
7,24,25
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C
8,15,17
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D
7,40,41
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Solution

The correct option is C 8,15,17
Let the lenght of hypotenuse of the triangle be xcm
Lenght of base of the triangle be ycm
Lenght of altitude of the triangle be zcm
According to given equation,
x=y+2 and x=2z+1
=>y=x2 and
=>z=x12
By Pythagoras Theorem
(AC)2=(AB)2+(AC)2
x2=y2+z2 (i)
putting values of y and z in equation (i) we get,
x2=(x2)2+(x12)2
=>x2=4(x2)2+(x1)24
=>4x2=4(x2+44x)+x2+12x
=>4x2=4x2+1616x+x2+12x
=>x218x+17=0
=>x217xx+17=0
=>x(x17)1(x17)=0
=>(x17)(x1)=0
Therefore,
x=17 or x=1
x=1 is not possible as base =x2=12=1cm which cannot be in negative.
Therefore,x=17
Putting the value in y
y=x2
y=172=15cm and
z=x12
z=1712
z=8cm
Therefore,
lenght of the sides of the triangle is 17cm,15cm,8cm.
212283_239616_ans.jpg

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