Question

one leg of a right triangle is 5 more than the other leg the hypotenuse is one more than twice the size of the short leg find the dimension of the triangle

Answer 1

Short leg be x

• Perpendicular=P=x
• Base=B=x+5
• Hypotenuse=H=2x+1

Apply Pythagorean theorem

`\\ \rm\Rrightarrow P^2+B^2=H^2`

`\\ \rm\Rrightarrow x^2+(x+5)¥2=(2x+1)^2`

`\\ \rm\Rrightarrow x^2+x^2+10x+25=4x^2+4x+1`

`\\ \rm\Rrightarrow 2x^2+10x+25=4x^2+4x+1`

`\\ \rm\Rrightarrow 4x^2-2x^2+4x-10x+1-25=0`

`\\ \rm\Rrightarrow 2x^2-6x-24=0`

`\\ \rm\Rrightarrow x^2-3x-12=0`

`\\ \rm\Rrightarrow x=(3\pm√(9+48))/(2)`

`\\ \rm\Rrightarrow x=(3\pm √(57))/(2)`

`\\ \rm\Rrightarrow x=(3\pm 7.2)/(2)`

`\\ \rm\Rrightarrow x=1.5\pm 3.6`

Take positive

`\\ \rm\Rrightarrow x=1.5+3.6=5.1`

• P=5.1
• B=10.1
• H=11.2