Question

If the length of the hypotenuse of a
right-angled triangle is 13 cm and
one side of the right- angled triangle
is 5 cm, what is the length of the
other side?
1 12 cm
2 9 cm
3 11 cm
4 12.5 cm​

Answer 1

Answer:

12 cm

Step-by-step explanation:

given :  1) the length of hypotenuse

           2) length of one of the other sides

to find : the length of 3rd side

Let the third side be x

By Pythagoras theorem

(13)^2 = 5^2 + x^2

169    = 25 + x ^2

x^2    = 169-25

x^2     = 144

x         =√144

x          = 12

Answer 2

Given :-

• Length of the Hypotenuse of a right-angled triangle = 13 cm
• One of the side of the right - angled triangle = 5 cm

To find :-

• Length of the other side

Solution :-

In ∆ABC

By pythagoras theorem,

→ H² = P² + B²

where,

• H = Hypotenuse (The longest side)
• P = Perpendicular
• B = Base

→ H = AC = 13 cm

→ P = AB = ?

→ B = BC = 5 cm

→ (AC)² = (AB)² + (BC)²

→ (13)² = AB² + (5)²

→ (13)² - (5)² = AB²

Using identity,

• (a - b)(a + b) = a² - b²

→ (13 - 5)(13 + 5) = AB²

→ (8)(18) = AB²

→ 144 = AB²

Taking square root on both the sides,

→ √144 = AB

→ ± 12 Reject - ve = AB

→ 12 = AB

AB = 12 cm

Therefore, length of the other side = 12 cm

Answer → Option (1) 12 cm

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Know MorE :-

Pythagoras theorem :-

In a right - angled triangle, the sum of the square of the hypotenuse is equal to the sum of the square of the other two sides.

• H² = P² + B²