Question

In a triangle ABC, measure of angle B is 90 degrees. AB is 3x-2 units and BC is x+3. If the area of the triangle is 17 sq cm, form an equation in terms of x and solve it.​

Answer 1

`x=(8)/(3)\ cm`

Explanation:

we know that

The area of the right triangle ABC is equal to

`A=(1)/(2)(AB)(BC)`

we have

`A=17\ cm^2`

`AB=(3x-2)\ cm`

`BC=(x+3)\ cm`

substitute the values

`17=(1)/(2)(3x-2)(x+3)`

`34=(3x-2)(x+3)`

`34=3x^2+9x-2x-6`

`3x^2+7x-6-34=0`

`3x^2+7x-40=0`

The formula to solve a quadratic equation of the form

`ax^(2) +bx+c=0`

is equal to

`x=\frac{-b(+/-)\sqrt{b^(2)-4ac}} {2a}`

in this problem we have

`3x^2+7x-40=0`

so

`a=3\\b=7\\c=-40`

substitute in the formula

`x=\frac{-7(+/-)\sqrt{7^(2)-4(3)(-40)}} {2(3)}`

`x=\frac{-7(+/-)√(529)} {6}`

`x=\frac{-7(+/-)23} {6}`

`x=\frac{-7(+)23} {6}=(16)/(6)=(8)/(3)`

`x=\frac{-7(-)23} {6}=-5`

therefore

The solution is

`x=(8)/(3)\ cm`