# 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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