Q68. - Algebra 1

Question

What is the perimeter of the triangle if $a=9$ and $b=10$

Step-by-Step Solution

Answer

The perimeter of the given triangle is 118 mm.

Step 1. Finding the perimeter of a triangle.

The perimeter of a triangle is defined as the sum of the length of all its three sides. If a triangle has sides of length a, b and c units then its perimeter is given by $(a+b+c)$ units.

Step 2. Example of finding the perimeter of a triangle.

Let the lengths of the sides of a triangle be given by $a,a^2,a+2$ units of length each.

Then the perimeter of the triangle is given by $(a+a^2+a+2)=a^2+2a+2$ units.

If $a=2mm$, then the perimeter is

$\begin{array}{l}=2^2+2\left(2\right)+2\\ =4+4+2\\ =10mm\end{array}$

Step 3. Description of step.

The perimeter of the given triangle can be expressed as $2a+0.5b^2+0.5b^2$.

It is given that, $a=9$ and $b=10$.

Substituting values of a and b in the above equation, the perimeter can be obtained as

$\begin{array}{l}2\left(9\right)+0.5{\left(10\right)}^2+0.5{\left(10\right)}^2\\ =18+0.5\left(100\right)+0.5\left(100\right)\\ =18+50+50\\ =118\text{ mm}\end{array}$

Hence, the perimeter of the given triangle is 118 mm.