Question

In an obtuse angled triangle, the sum of the squares on the sides making the obtuse angle is

• A. less than the square on the third side
• B. greater than the square on the third side
• C. equal to the square on the third side
• D. none of these

Answer 1

The correct option is A less than the square on the third side

The triangle is an obtuse triangle if the sum of the squares of the smaller sides is less than the square of the largest side.

Let $ABC$ is an obtuse triangle.

$\angle B={120}^o$

$AB=5cm,BC=4cm$ and $AC=8cm$

$\Rightarrow$ $(AC{)}^2=(8{)}^2=64$ ---- ( 1 )

$\Rightarrow$ $(AB{)}^2+(BC{)}^2=(5{)}^2+(4{)}^2=25+16=41$ ---- ( 2 )

From ( 1 ) and ( 2 ) we can see,

$\Rightarrow$ $(AB{)}^2+(BC{)}^2<(AC{)}^2$

Hence, In an obtuse angled triangle, the sum of the squares on the sides making the obtuse angle is less than the square on the third side.