Question

A DEF is a right angled triangle. If DE = 9 cm, EF = 12 cm,E= 90°, find DF.​

Answer 1

✬ DF = 15 cm ✬

Step-by-step explanation:

Given:

• DEF is a right angled triangle.
• DE = 9 cm , EF = 12 cm
• Meaure of ∠DEF is 90°.

To Find:

• What is the meaure of DF?

Solution: Here in right angled triangle DEF, We have

• DE = Perpendicular
• ∠DEF = 90°
• EF = Base
• DF = Hypotenuse

Using Pythagoras Theorem in ∆DEF

★ H² = P² + B² ★

$\implies{\rm }$ DF² = DE² + EF²

$\implies{\rm }$ DF² = 9² + 12²

$\implies{\rm }$ DF² = 81 + 144

$\implies{\rm }$ DF² = 225

$\implies{\rm }$ DF = √225

$\implies{\rm }$ DF = 15

Hence, the meaure of DF is 15 cm.

Answer 2

DF = 15cm.

SOLUTION :-

In right angled ΔDEF, ∠DEF = 90° .

• Applying Pythagoras theorem,

=> DF² = DE² + EF²

=> DF² = 9² + 12²

=> DF² = 81 + 144

=> DF² = 225

=> DF = √225

=> DF = 15

.°. DF = 15 cm.

LEARN MORE :-

• Pythagoras theorem .

In a right angled triangle the square of the length of the hypotenuse of a right triangle is equal to the sum of the squares of the lengths of the other sides.

• Converse of Pythagoras theorem .

If the square of the length of the longest side of a triangle is equal to the sum of the squares of the other two sides, then the triangle is a right triangle.