Question

the sides of a right angled triangle containing the right angle are 3(x+1)cm and (2x-1)cm . if the area is 30sqcm , find the lengths of the sides

Answer 1

Answer:

Lengths of the sides of the triangle are 12 cm, 5 cm, 13 cm

Step-by-step explanation:

The sides of a right angled triangle containing the right angle are 3(x+1)cm and (2x-1)cm . if the area is 30sqcm , find the lengths of the sides

Given:

$\text{Area of right triangle}=30\:cm^2$

$\frac{1}{2}\times3(x+1)\times(2x-1)=30$

$\implies\:3(x+1)\times(2x-1)=60$

$\implies\:(x+1)\times(2x-1)=20$

$\implies\:2x^2-x+2x-1-20=0$

$\implies\:2x^2+x-21=0$

$\implies\:2x^2+7x-6x-21=0$

$\implies\:x(2x+7)-3(2x+7)=0$

$\implies\:(x-3)(2x+7)=0$

$\implies\:x=3,\frac{-7}{2}$

But x cannot be negative

$\text{The suitable value of x is 3}$

3(x+1)=3(3+1)=12 cm

2x-1=2(3)-1=5 cm

Now,

$\text{Hypotenuse}=\sqrt{12^2+5^2}$

$\text{Hypotenuse}=\sqrt{144+25}=\sqrt{169}=13\:cm$