The height and base of a triangle are equal to the length and breadth of a rectangle respectively. If the perimeter of the rectangle is 86m and the difference between its length and breadth is 5m, what is the area of the triangle ? (in m^{2} )
The height and base of a triangle are equal to the length and breadth of a rectangle respectively. If the perimeter of the rectangle is 86m and the difference between its length and breadth is 5m, what is the area of the triangle ? (in m^{2} )
1). 224
2). 228
3). 216
4). 242
2 answers
Let length of rectangle = $x$ m
Breadth = $(x - 5)$ m
=> Perimeter of rectangle = $2 (x + x - 5) = 86$
=> $2x - 5 = \frac{86}{2} = 43$
=> $2x = 43 + 5 = 48$
=> $x = \frac{48}{2} = 24$
=> Breadth = 24 - 5 = 19 m
=> Height of triangle = 24 m and Base of triangle = 19 m
$\therefore$ Area of triangle = $\frac{1}{2} \times 24 \times 19$
= $12 \times 19 = 228 m^2$
Let length of rectangle = $x$ m
Breadth = $(x - 5)$ m
=> Perimeter of rectangle = $2 (x + x - 5) = 86$
=> $2x - 5 = \frac{86}{2} = 43$
=> $2x = 43 + 5 = 48$
=> $x = \frac{48}{2} = 24$
=> Breadth = 24 - 5 = 19 m
=> Height of triangle = 24 m and Base of triangle = 19 m
$\therefore$ Area of triangle = $\frac{1}{2} \times 24 \times 19$
= $12 \times 19 = 228 m^2$