CameraIcon
CameraIcon
SearchIcon
MyQuestionIcon
MyQuestionIcon
Question

A right-angle triangle has a hypotenuse of length Qcm and one side of length Pcm. If Q-P=2 express the length of the third side of the right-angle triangle in terms of Q.


Open in App
Solution

Express the third side in terms of Q.

According to the Pythagoras theorem, In a right-angle triangle, the square of the hypotenuse is equal to the sum of the square of the other two sides.

Here, Pcm is the length of the hypotenuse and Q is one of the other sides of right angle triangle.

Assume x the the third side of the triangle.

Find the length of the third side of the right-angle triangle in terms of Q:

Q2=P2+x2[bypythagorastheorem]x2=Q2-P2x2=(Q-P)(Q+P)x2=2(Q+P)[Q-P=2]x2=2(Q+Q-2)x2=4Q-4x2=4(Q-1)x=4(Q-1)x=2Q-1

Hence, the third side length is 2Q-1.


flag
Suggest Corrections
thumbs-up
3
BNAT
mid-banner-image