Chapter ISG, Problem 8.6.1.3P

To determine

To find the dimensions of triangle.

Answer to Problem 8.6.1.3P

Base is 10

Height is 20

Explanation of Solution

Given information:

Area of triangle is 100.

And its height is 10 feet more than its base.

Formula used:

Area of triangle $=\frac{1}{2}\times base\times height$

Calculation:

Let base of the triangle is $x$

So,height of the triangle is $x+10$

Substituting the values in the formula

Area of triangle $=\frac{1}{2}\times x\times (x+10)$

According to question,Area of triangle is 100

  $100=\frac{1}{2}\times x\times (x+10)$

On solving,

  $100=\frac{1}{2}(x^2+10x)$

On cross multiplying

  $200=x^2+10x$

So,

  $x^2+10x-200=0$

Split the middle term so that its addition comes out to be $+10x$

And its multiplication $x^2\times 200$ which is equalsto $200x^2$

  $x^2-10x+20x-200=0$

Taking common,

  $x(x-10)+20(x-10)=0$

Therefore,

  $(x+20)(x-10)=0$

Using the Zero Product Property ,

  $(x+20)=0$ or $(x-10)=0$

So,

  $x+20=0$

Or

  $x=-20$

Also,

  $x-10=0$

So,

  $x=10$

So, $x=-20$ and $x=10$ base can never be negative

Therefore, base is 10

So, height is 20