# If the area of triangle A, with sides of 6, 8, and 10, equals the area of rectangle B, with width of 4, what is the perimeter of the rectangle?

Jun 23, 2016

Perimeter of rectangle is $2 \left(4 + 6\right) = 20 \text{ } u n i t s$

#### Explanation:

$\textcolor{b l u e}{\text{Determine the area of the triangle}}$

Using Herons Law for area of the triangle

Let the sides of the triangle be {a;b;c} |->{6,8,10}

Let $s$ be a constant where $s = \frac{a + b + c}{2}$

Thus area$= \sqrt{s \left(s - a\right) \left(s - b\right) \left(s - c\right)}$

$a r e a = \sqrt{12 \left(12 - 6\right) \left(12 - 8\right) \left(12 - 10\right)} = 24 {\text{ units}}^{2}$
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$\textcolor{b l u e}{\text{Determine the perimeter of the rectangle}}$
Let the unknown length of the rectangle be $x$.

Area of rectangle is the product of width and height

$\implies 24 = 4 \times x \text{ "=>" } x = 6$

Perimeter of rectangle is $2 \left(4 + 6\right) = 20 \text{ } u n i t s$

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$\textcolor{b l u e}{\text{ Another approach for area}}$
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If you divide all the triangle side measurement by 2 you end up with: 3; 4; 5

This is a standardised right triangle used by in many contexts: One such example could be a builder setting out the corners of a house.

color(green)("Knowing this is a right triangle: area "= 1/2 xx 6xx8=24