What procedure would you use to square a given triangle? Here, the task is to construct a square Class 9

What procedure would you use to square a given triangle? Here, the task is to construct a square Class 9

Question 1.

What procedure would you use to square a given triangle? Here, the task is to construct a square whose area is equal to the area of some given triangle. Think carefully. How would you proceed ? Class 9

Answer:

i. Draw the triangle ABC and choose one side as the base. Let BC be the base.

ii. Draw the perpendicular from vertex A to BC. Let the height be h.

iii. Construct a rectangle having:

Length as base BC = b, and

breadth $\frac{h}{2}$.

The area of this rectangle is:

Area of rectangle = b × $\frac{h}{2}$ = $\frac{1}{2}$bh

which is equal to the area of the given triangle.

iv. Now use Baudhayana method for squaring a rectangle to construct a square equal in area to this rectangle.

v. The obtained square will therefore have the same area as the given triangle.