Question

Find the answer in terms of x.​

Answer 1

Answer:

Step-by-step explanation:

ΔABC is an isosceles right angled triangle, with right angle at B.

Hence ∠A and ∠C  should be 45°.

Now consider the right angled triangle ΔAOB, which is right angled at O.

We know that ∠A = 45°, ∠O = 90° , ∠ABO = 45°.

Thus this is also an Right angled Isosceles triangle.

In isosceles triangle, sides opposite to equal angles are equal.

So since OA = 1, OB must also be equal to 1.

Thus co-ordinates of B are (0,1)

Slope of line AB = 0 - 1 / 1 - 0 = -1.

The equation of line AB is of form y = mx + b  

=> y = -1 * x +  1  (b nothing but y-intercept which is y).

=> y = 1 - x

Hence the co-ordinates of P are P(x , 1 -x).

Now to find Area of rectangle:

Length of rectangle = 2x

Width of rectangle = y = 1 - x.

Hence area of Rectangle = L * B = x * (1 - x)

                                                      = x - x²