Question

The hypotenuse of a right triangle is 3√5 cm . If the small side is triple and longer side is double the new hypotenuse will be 15 cm.Find the length of each side

Answer 1

the answer is shown below:

Answer 2

Let smaller side = x CM

Larger side = y CM

Hypotenuse = 3√5cm

By Pythagoras theorem

$\longrightarrow$$\sf\green{ {x}^{2} + {y}^{2} = {(3 \sqrt{5}) }^{2} }$

$\longrightarrow$$\sf\green{{x}^{2} + {y}^{2} = 45}$

$\longrightarrow$$\sf\green{{y}^{2} = 45 - {x}^{2} }$

When the smaller side is tripled and the larger side is doubled, the hypotenuse becomes 15cm.

$\therefore$ $\sf\red{( {3x}^{2} ) - ( {2y)}^{2} = {15}^{2}}$

$\longrightarrow$$\sf\red{ {9x}^{2} + 4(45 - {x)}^{2} = 225}$

$\longrightarrow$$\sf\red{ {5x}^{2} = 225 - 180 = 45}$

$\longrightarrow$$\sf\red{ {x}^{2} = 9}$

$\longrightarrow$$\sf\red{x = ±3}$

As the side of a triangle cannot be negative,

x ≠ -3 , so x = 3

Hence, the length of the smaller side us 3cm and the length of the larger side is 6cm.