Answer:
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
Answer:
20
Step-by-step explanation:
We use the Pythagorean Theorem to verify that triangle $ABC$ is a right triangle, or we recognize that $(6,8,10)$ is a multiple of the Pythagorean triple $(3,4,5)$. The area of a right triangle is $\frac{1}{2}bh$ where $b$ and $h$ are the lengths of the two legs, so the area of triangle $ABC$ is $\frac{1}{2}(6)(8)=24$. If the area of the rectangle is $24$ square units and the width is $4$ units, then the length is $\frac{24}{4}=6$ units. That makes the perimeter $6+6+4+4=\boxed{20}$ units.
