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Question

ABC is an isosceles right angle triangle, right angled at B. The ratio of the sides AB: BC : AC is .

A
1:1:2
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B
2:1:1
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C
3:2:1
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D
1:2:3
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Solution

The correct option is A 1:1:2

Let us assume the length of side AB of the triangle to be x units.
Applying trignometric ratios to the sides, we get :
sin 45=(xAC)12=(xAC)AC=x2 ...(i)Similarly,tan 45=(xBC)1=(xBC)BC=x ...(ii)
So, the ratios of the sides of the triangle with angles 45,45& 90=x:BC:AC
=x:x:x2(from (i)&(ii))
=1:1:2

An alternate and shortcut method of solving this question is:

For the given triangle, as two angles are equal; the two sides opposite to these angles will also be equal.
And as the third angle is 90, the triangle is right - angled triangle.
Let us assume the length of the equal sides is equal to x units.
So, length of the hypotenuse = (x2+x2) = x2
So, Ratio of the sides of the triangle = x : x : x2
Ratio of the sides of the triangle = 1 : 1 : 2

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