What is the area of the largest triangle that can be fitted into a rectangle of length L units and width w units?
(a) Lw/2
(b) Lw/3
(c) Lw/6
(d) Lw/4
Solution:
As evident from the diagram, infinite triangles can be constructed inside the rectangle. The diagram below depicts some triangles from the infinite possibilities:
The area of the triangle = (1/2)(base)(height)
The triangles in the above diagram can have L or w as either height or base of the triangle. In either case the area of the triangle is:
Area of triangle = (½) × (L) × (w)
The maximum height possible is L or w and the maximum base possible is L or w. If maximum height possible is L then the maximum base possible is w. If maximum height possible is w then maximum base possible is L.
In both scenarios the maximum area of a triangle will be (½) × (L) × (w) .
The correct answer is (a).
✦Try This: What will be area of the square in which the circle of radius r is inscribed? (a)πr² (b) 4r² ( c) 2r² (d) r²
The circle inscribed in the square is shown below. If the radius of the circle is r then the diameter is 2r which also is the side of the square inscribing the circle.
The area of the square will be therefore = (2r) × (2r) = 4r²
Hence the correct answer is choice (b).
☛ Also Check: NCERT Solutions for Class 8 Maths Chapter 11
NCERT Exemplar Class 8 Maths Chapter 11 Problem 4
What is the area of the largest triangle that can be fitted into a rectangle of length L units and width w units? (a) Lw/2 (b) Lw/3 (c) Lw/6 (d) Lw/4
Summary:
The area of the largest triangle that can be fitted into a rectangle of length L units and width w units is (½)Lw
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