Question

triangle abc has sides 10, 24, and 26 cm long. a rectangle that has an area equal to that of the triangle is 3 cm wide. find the perimeter of the rectangle.

the perimeter of the rectangle is \boxed{} cm.

Explanation:

Step1: Identify triangle type, find area

First, confirm it's a right triangle: $10^2 + 24^2 = 100 + 576 = 676 = 26^2$.
Area of triangle: $\frac{1}{2} \times 10 \times 24 = 120$ cm²

Step2: Find rectangle length

Set rectangle length as $l$. Area = $l \times 3 = 120$, so $l = \frac{120}{3} = 40$ cm

Step3: Calculate rectangle perimeter

Perimeter formula: $2 \times (length + width)$
$2 \times (40 + 3) = 2 \times 43$

Answer:

86 cm