Question

which of the following measurements could be the side lengths of a right triangle?

Answer 1

Answer:

Option A

Step-by-step explanation:

Here we need to tell which could be the side lengths of a right angled triangle . As we know that in a right angled triangle , the sum of square two sides along the right angle is equal to the square of side opposite to right angle .

That is ,

$\longrightarrow a^2 = b^2+ c^2$

$\begin{picture}(8,8)\setlength{\unitlength}{1cm} \thicklines\put(0,0){\line(1,0){4}}\put(4,0){\line(0,1){3}}\put(4,3){\line(-4,-3){4}}\put(2,-0.5){ \sf \sqrt{48}in }\put(4.4,1.5){ \sf \sqrt{12}in. } \put(1.2,2){ \sf \sqrt{60}in. }\end{picture}$

We can start by looking at the options , first option is ,

$\longrightarrow \sqrt{48}\ in , \sqrt{12}\ in , \sqrt{60} in$

So by squaring first two sides and adding them , we have ,

$\longrightarrow (\sqrt{48})^2+(\sqrt{12})^2$

$\longrightarrow 48+12 = 60$

And by squaring the third side we have ,

$\longrightarrow \sqrt{60}^2 = 60$

Hence here the sum of square of two sides is equal to the square of third side .

Therfore the triangle with sides √48 in , √12in and √60 forms a right angle ∆.