Question

I cant figure it out :( pls help me

Answer 1

Explanation:

if abc≅def then ac≅df, ab≅de, and bc≅ef.

then use pythagorean theorem:

df²=de²+ef²

9²=4.5²+ef²

81=20.25+ef²

ef=\sqrt[60.75]

Answer 2

• EF = 7.79423 feet or approximately 7.80 feet.

Solution :

As, we are given :

• ∆ABC ≅ ∆DEF
• AB = 4.5 feet
• AC = 9 feet
• ∠B = 90° ( from diagram)
• ∠E = 90° (from diagram)

We have to find :

• Length of EF = ?

As, we have ∆ABC ≅ ∆DEF, thus all corresponding sides and angles are equals.

• AB = DE = 4.5 feet
• BC = EF
• AC = DF = 9 feet
• ∠A = ∠D
• ∠B = ∠E = 90°
• ∠C = ∠F

Now, in ∆DEF, we have

• DE = 4.5 feet
• DF = 9 feet
• ∠E = 90°

So, we can find the side EF by using Pythagoras theorem, which is :

• (Hypotenuse)² = (Base)² + (Perpendicular)²

In ∆DEF,

• Hypotenuse, DF = 9 feet
• Perpendicular, DE = 4.5 feet
• Base, EF = ?

=> (9 feet)² = (EF)² + (4.5 feet)²

=> 81 feet² = (EF)² + 20.25 feet²

=> 81 feet² - 20.25 feet² = (EF)²

=> 60.75 feet² = (EF)²

=> EF = √60.75 feet = 7.79423

Hence, Side EF = 7.79423 feet or almost 7.80 feet.