If a right-angled triangle has shorter sides of lengths 5 cm and 12 cm, then what is the length of its hypotenuse? Class 8

If a right-angled triangle has shorter sides of lengths 5 cm and 12 cm, then what is the length of its hypotenuse? Class 8

Question 1.

If a right-angled triangle has shorter sides of lengths 5 cm and 12 cm, then what is the length of its hypotenuse? First draw the right-angled triangle with these sidelengths and measure the hypotenuse, then check your answer using Baudhayana’s Theorem. Class 8

Solution:

On measurement hypotenuse,

PR = 13 cm.

By Baudhayana-Pythagoras theorem,

PR² = PQ² + QR²

= 5² + 12² = 25 + 144 = 169

So, PR = [latex]\sqrt{169}[/latex] = 13 cm. (Checked)

Question 2.

If a right-angled triangle has a short side of length 8 cm and hypotenuse of length 17 cm, what is the length of the third side?

Again, try drawing the triangle and measuring, and then check your answer using Baudhayana’s Theorem. Class 8

Solution:

Do as directed.

Let length of the third side be x cm. Then, Baudhayana-Pythagoras theorem,

17² = 8² + x²

or 289 = 64 + x²

or x² = 289 - 64 = 225.

So, x = [latex]\sqrt{225}[/latex] = 15 cm.