Question

The hypoenuse of a right triangle is 25 cm. We know that the difference in lengths of the other two sides is 5 cm. We would like to find out the length of the two sides ?​

Answer 1

Gíνєn :

• The hypoenuse of a right triangle is 25 cm.

• We know that the difference in lengths of the other two sides is 5 cm.

Tσ Fínd :

• Length of Two sides

Sσlutíσn :

✩ Here in the Question we are given Hypotenuse of traingle 25cm i.e Shorter side. so, let the short side be 25cm. and Difference in Lengths of other two sides is 5 cm. Let the Longer side be x + 5 cm. By using Pythagoras theorem We will find the Required Length of the sides of the right Triangle

• Let Shorter Side = x cm
• Longer Side = (x + 5) cm

Using pythagoras theorem

➢ (x)² + (x + 5)² = (25)²

➢ x² + x² + 10 = 625

➢ 2x² + 10x - 600 = 0

➢ x² + 5x - 300 = 0

➢ (x + 20) (x - 15) = 0

Now, Value of x

➢ x + 20 = 0

➢ x = -20 (Reject)

➢ x - 15 = 0

➢ x = 15

____________

• Shorter Side = 15cm

• Longer Side = 15 + 5 = 20cm

∴ Length of two sides is 15 and 20cm.