Chapter 8.4, Problem 47AYU

(a)

To determine

To find: Whether the triangles with the given sides are perfect or not.

Answer to Problem 47AYU

The triangle is perfect as the area and the perimeter is same.

Explanation of Solution

Given:

The given sides are $\left(9,10,17\right)$ .

Calculation:

Consider the semi perimeter for the ground of the building is,

  $\begin{array}{c}s=\frac{1}{2}\left(9+10+17\right)\\ =18\end{array}$

Consider the formula for the area of the triangle is,

  $\begin{array}{c}K=\sqrt{18\left(18-9\right)\left(18-10\right)\left(18-17\right)}\\ =\sqrt{18\left(9\right)\left(8\right)\left(1\right)}\\ =36\end{array}$

The area and the perimeter of the triangles are same so the triangle is perfect.

(b)

To determine

To find: Whether the triangles with the given sides are perfect or not.

Answer to Problem 47AYU

The triangle is perfect as the area and the perimeter is same.

Explanation of Solution

Given:

The given sides are $\left(6,25,29\right)$ .

Calculation:

Consider the semi perimeter for the ground of the building is,

  $\begin{array}{c}s=\frac{1}{2}\left(\left(6+25+29\right)\right)\\ =30\end{array}$

Consider the formula for the area of the triangle is,

  $\begin{array}{c}K=\sqrt{30\left(30-6\right)\left(30-25\right)\left(30-29\right)}\\ =\sqrt{30\left(24\right)\left(5\right)\left(1\right)}\\ =\sqrt{3600}\\ =60\end{array}$

The area and the perimeter of the triangles are same so the triangle is perfect.