Question

In right angled triangle , length of hypotenuse is 30cm and length remaining sides is 4x and 3x. Determine the length of two sides

Answer 1

Hypotenuse = 30 cm

Height = 4x

Breadth = 3x

By Pythagoras theorom,

Hypotenuse^2 = Height^2 + Breadth^2

30^2 = (4x)^2 + (3x)^2

900 = 16x^2 + 9x^2

Therefore,

25x^2 = 900

x^2 = 900/25 = 36

x = √36 = 6

x = 6 cm

Therefore,

Height = 4x = 4 x 6 = 24 cm

Breadth = 3x = 3 x 6 = 18 cm

Answer 2

$\huge \red { \boxed{ \boxed{ \mathsf{ \mid \ulcorner Answer : \urcorner \mid }}}}$

Hypotenuse (H) = 30 cm

Base = 3x

Height = 4x

========================

Use Pythagoras Theorem :-

$\huge{\boxed{\boxed{\green{\sf{H^{2} \: = \: B^2 \: + \: P^2}}}}}$

_________________[Put Values]

(30)² = (3x)² + (4x)²

900 = 9x² + 16 x²

900 = x²(16 + 9)

900 = x²(25)

x² = 900/25

x² = 36

x = √36

x = 6 cm

_______________________________

Base = 3x = 3(6) = 18 cm

Height = 4x = 4(6) = 24 cm