Question

# If the area of a parallelogram is 300m^{2} and the base of the parallelogram is thrice its height, find the base and height of a parallelogram.

Hint:

### given the area of parallelogram is given ; condition between base and height is

given .now, substitute them in the formula area of parallelogram = base × height to

find the base and height of parallelogram.

## The correct answer is: height = 10 m , base = 30 m.

### Ans :- height = 10 m , base = 30 m.

Explanation :-

Given , area of parallelogram = 300 sq.m

Let the height of parallelogram be x

Then by the condition we get base of parallelogram = 3x

Area of parallelogram = base × height = 3x × x = 3 x^{2 }= 300 m^{2}.

We get, x^{2 }= 100 m^{2 }x= 10 m

3x = 3 × 10 = 30 m

Therefore , the height of parallelogram = 10 m and base of parallelogram = 30 m.

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length 10 m. If the seating portion of the hall has an area of 180 square meters, what is the value of *x *?

**Note:**

There are different concepts used to solve this problem. Another concept used which is not mentioned in the hint is that the perpendicular drawn from the vertex of an isosceles triangle to the

base cuts the base in half. This property is also applicable in equilateral triangles as they are a special case of isosceles triangle.