Math, asked by spujitha217643, 7 days ago

The altitude of a parallelogram is twice of the length of base and its area is 900cm^2. The length of base and altitude respectively are​

Answers

Answered by Agent0009
0

Answer:

x = 15\sqrt{2} m. -----> length

2x = 30\sqrt{2} m -----> altitude

Step-by-step explanation:

The altitude is just a fancy word that means the height of a parallelogram.

Let the length of the base of a parallelogram be x.

Since the height is twice the length of the base, it is 2(x) = 2x.

Now, we know that base times height gets us the area of a parallelogram.

x(2x) = 900

2x^2 = 900

Let us divide both sides by 2 to get rid of the coefficient on the LHS.

x^2 = 450

Now, when we take the square root of both sides,

x = \sqrt{450}

Let us simplify this expression in the square root, such that it involves one perfect square and another imperfect square.

450 = 3 x 150 = 3 x 50 x 3 = 50 x 9.

Now, 9 is a perfect square.

So, x can be written as 3\sqrt{50}.

This can be simplified further.

50 = 25 x 2.

25 is a perfect square.

x = 3\sqrt{50} = 3\sqrt{25(2)} = 3(5)\sqrt{2} = 15 \sqrt{2}

This cannot be simplified further.

x = 15\sqrt{2} m. -----> length

2x = 30\sqrt{2} m -----> altitude

Similar questions