Question

The length of the sides forming right angle of a right angled triangle are 5x cm and (3x -1) cm. If the area of the triangle is 60 sq.cm., find its hypotenuse.

Answer 1

answer is hypotenuse =17cm

Answer 2

Hypotenuse of the triangle is 17 cm.

Step-by-step explanation:

Given :-

The length of the sides forming right angle of a right triangle are 5x cm and (3x-1) cm.

Area of the triangle is 60 cm².

To find :-

Hypotenuse of the triangle.

Solution :-

Let the hypotenuse of the triangle be y cm.

And,

let the perpendicular of the triangle be 5x cm and the base of the triangle be (3x-1) cm.

Formula used :

${\boxed{\sf{Area\:of\: right\: triangle=\dfrac{1}{2}\times\:base\times\: perpendicular}}}$

According to the question ,

$\begin{gathered}\to \sf \: \dfrac{1}{2} \times (3x - 1) \times 5x = 60 \\ \\ \to \sf \: (3x - 1)5x = 120 \\ \\ \to \sf \: 15x^{2} - 5x = 120 \\ \\ \to \sf \: 5(3 {x}^{2} - x) = 120 \\ \\ \to \sf \: 3 {x}^{2} - x = 24 \\ \\ \to \sf \: 3 {x}^{2} - x - 24 = 0 \\ \\ \to \sf \: (x - 3)(3x + 8) = 0\end{gathered}$

Either,

x - 3 = 0

→ x = 3

Or,

3x+8=0

→ x = -8/3 [ Impossible]

Therefore,

Perpendicular = 5×3 = 15 cm

Base = (3×3-1) = 8 cm

Now find the hypotenuse by using Pythagoras Theorem.

Hypotenuse² = Perpendicular ² + Base²

→ y ² = 15² + 8²

→ y ² = 225+64

→ y=√289

→ y = 17

Therefore, the hypotenuse of the triangle is 17 cm.