The area of a rectangle is equal to area of a right-angle triangle. The…
2025
The area of a rectangle is equal to area of a right-angle triangle. The breadth of the rectangle is 18 cm and the base of the triangle is 8 cm more than the length of the rectangle and height of the triangle is 3 cm more than length of the rectangle. Find length (in cm) of the rectangle (length > breadth)
- A.
36
- B.
24
- C.
21
- D.
12
- E.
40
Attempted by 7 students.
Show answer & explanation
Correct answer: B
Let the rectangle length be L. Rectangle area = 18L.
Triangle base = L + 8 and height = L + 3, so triangle area = (L + 8)(L + 3)/2.
Equating areas gives 36L = (L + 8)(L + 3), so L^2 - 25L + 24 = 0.
L = 24 or 1, and length is greater than breadth, so L = 24 cm.