Rectangle and triangle...
A rectangle and a triangle have the same area. When placed on the same level, the tip of the triangle touches the top edge of the rectangle. What is the base of the triangle if the area of the rectangle is 150 square cm?
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By the given discrpition the triangle has the same altitude from its base as a distance between the two parallel sides of the rectangle.
Let this altitude of the triangle be h.
Area of the rectangle = 150 sq cm, given.
Therefore the base of the rectangle = 150/h.
Since the triangle has the same area as that of the rectangle, the base 150 sq cm = (1/2) *base*height.
150 = (1/2) base of triangle *h.
base of the triangle = 2*150/h = 2(base of rectangle).
Therefore the base of the triangle is twice the base of rectangle.
The area of a rectangle is given by the relation length* width. The area of a triangle is given by the relation (1/2)*base* height.
Now we know that the two have the same area equal to 150 cm^2. Also, when placed on the same level the tip of the triangle touches the upper edge of the rectangle. So we can say that one of the sides of the rectangle is equal to the height of the triangle.
Let the side of the rectangle be x. Therefore the other side is 150/x. Also x= height. So (1/2)* base*x = 150
It is not possible to calculate x as we have two variables and can only construct one equation.
Therefore we cannot find the base of the triangle using the information given.
Neela's answer is excellent.
For the triangle (whose height is the breadth of rectangle) to be having the same area as the rectangle, the base has to be twice as long as the length of the rectangle.
[ Comparing the formula for area of rectangle (length x breadth) and area of triangle (1/2 x base x height), for these two expressions to be equal when the breadth of rectangle is equal to height of triangle, it follows that base has to be 2xlength of rectangle ]
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