Chapter 8, Problem 6PFA

To determine

To find the expression for area of the garden.

Answer to Problem 6PFA

  $\frac{1}{2}(21x^2+36x-81)$

Explanation of Solution

Given:

  

Formula used:

  $\text{Area of a triangle}=\frac{1}{2}(b\times h)$

Calculation:

From the given figure,

  $\text{Height of the triangle}=(7x-9)$

  $\text{Base of the triangle}=(3x+9)$

Substituting the above values in the area of the triangle,

  $\begin{array}{c}\text{Area of a triangle}=\frac{1}{2}((7x-9)\times (3x+9))\\ =\frac{1}{2}((7x\times 3x)+(7x\times 9)+(-9\times 3x)+(-9\times 9))\\ =\frac{1}{2}(21x^2+63x-27x-81)\\ =\frac{1}{2}(21x^2+36x-81)\end{array}$

Conclusion:

Therefore, the area of the triangle is $\frac{1}{2}(21x^2+36x-81).$