Triangle $ABC$ has sides of $6$ units, $8$ units, and $10$ units. The width of a rectangle, whose area is equal to the area of the triangle, is $4$ units. What is the perimeter of this rectangle, in units

20

Step-by-step explanation:

Given that the area of the rectangle is equal to that of the triangle

Area of triangle $ABC$

= 1/2 (bh)

Given that the sides of the triangle are $6$ units, $8$ units, and $10$ units,

The base and the heights are $6$ units and $8$ units. The $10$ units is the hypotenuse

From Pythagoras theorem,

6^2 + 8^2 = 10^2

Therefore, area of triangle

=1/2 (6 * 8)

= $24$ units^2

Area of rectangle = L * W

Where L = Length, W = Width

Area of the rectangle = area of triangle

L * 4 = 24

L = 24/4

L = $6$ Units

Perimeter of rectangle

=2 (L + B)

= 2 (6 + 4)

= $20$ Units