Question

A triangle DEF is right-angled at E, with DE =6.7 m and EF = 5.5 m. Find the length of DF.​

Answer 1

★ How to do :-

Here, we are given with a diagram consisting a right-angled triangle in which we are provided with the measurements of two of it's sides. We are nit given with the measurement of an other side which is named as DF. We are asked to find the value of that side. In the diagram we can observe that the value of the hypotenuse side is not given which is named as DF. The concept used in this problem is called as Pythagoras theorem. It can be used here. So, let's solve!!

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➤ Solution :-

${\tt \leadsto \underline{\boxed{\tt {de}^{2} + {ef}^{2} = {df}^{2}}}}$

${\tt \leadsto {6.7}^{2} + {5.5}^{2} = {df}^{2}}$

${\tt \leadsto 44.89 + 30.25 = {df}^{2}}$

${\tt \leadsto 75.14 = {df}^{2}}$

${\tt \leadsto df = \sqrt{75.14}}$

$\Huge\therefore$ The value of the side DF is √75.14.

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More to know :-

• The Pythagoras property is the rule which was invented by a scientist named as Pythagoras. He proved this rule and his name was given to this property.
• This rule says that the hypotenuse of the right angled triangle always measures as the sum of square of the measurements of other two sides.

Answer 2

Question :

A triangle DEF is right angled at E ,with DE = 6.7 m and EF = 5.5 m. Find the length of DF.

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Given :

• DEF is right angled triangle.
• < E = 90°
• DE = 6.7 m
• EF = 5.5 m

To find :

• Length of DF.

Theorem to be used :

• Pythagoras theorem.

Solution :

↝ Pythagoras Theorem states that Square of hypotenuse is equal to sum of perpendicular square and base square.

→ H² = P² = B²

➟ (DF)² = (6.7)² + (5.5)²

➟ (DF)² = 44.89 + 30.25

➟ (DF)² = 75.14

➟ DF = √75.14

↬ THEREFORE, LENGTH OF SIDE DF = √75.14 m.