Question

sides of triangles at given below determine which of them are right triangle writ the length its hypotenuse (1) 7cm (2) 24 cm 25 cm (2) 3cm 8cm 6cm (3) 50cm 80cm 10cm (4) 13cm 12cm 5cm​

Answer 1

Answer:

(i)

Since, (25)2=(7)2+(24)2⇒625=49+576⇒625=625

Hence, 7cm, 24cm and 25cm are the sides of Right Angled Triangle and its Hypotenuse is 25cm

(ii)

Since, (8)2=(3)2+(6)2⇒64=45

Hence, 8cm, 6cm and 3cm do not form Right Angled Triangle.

(iii)

Since, (100)2=(50)2+(80)2⇒10000=8900

Hence, 100cm, 50cm and 80cm do not form Right Angled Triangle.

(iv)

Since, (13)2=(12)2+(5)2⇒169=144+25⇒169=169

Hence, 13cm, 12cm and 5cm are the sides of Right Angled Triangle and its Hypotenuse is 13cm.

Answer 2

Proper question:

Sides of triangles are given below determine which of them are right triangle and also write that what is hypotenuse

(1) 7 cm, 24 cm and 25 cm

(2) 3 cm, 8 cm and 6 cm

(3) 50 cm, 80 cm and 10cm

(4) 13 cm, 12 cm and 5 cm

Using concept:

• Phythagoras Theorm

${\small{\underline{\boxed{\sf{\star \: (Hypotenuse)^{2} \: = (Perpendicular)^{2} \: + (Base)^{2}}}}}}$

We can write Hypotenuse as H, Perpendicular as P and Base as B.

Knowledge required:

→ In a right angled triangle the longest side is the hypotenuse.

→ It the square of hypotenuse and the sum of square of both base and perpendicular came same then it triangle is a right angled triangle.

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Solution first!

↪️ (H)² = (P)² + (B)²

↪️ (25)² = (24)² + (7)²

↪️ 625 = 576 + 49

↪️ 625 = 625

Therefore, it is a right angled triangle!

The length of hypotenuse is 25 cm!

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Solution second!

↪️ (H)² = (P)² + (B)²

↪️ (8)² = (6)² + (3)²

↪️ 64 = 36 + 9

↪️ 64 ≠ 45

Therefore, it isn't a right angled triangle!

The length of hypotenuse is 8 cm!

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Third solution!

↪️ (H)² = (P)² + (B)²

↪️ (80)² = (50)² + (10)²

↪️ 6400 = 2500 + 100

↪️ 6400 ≠ 2600

Therefore, it isn't a right angled triangle!

The length of hypotenuse is 80 cm!

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Fourth solution!

↪️ (H)² = (P)² + (B)²

↪️ (13)² = (12)² + (5)²

↪️ 169 = 144 + 25

↪️ 169 = 169

Therefore, it is a right angled triangle!

The length of hypotenuse is 13 cm!

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