Question

The length of the base a right angle triangle is 2x units and its area is 4x^2+4 Find the length of
the perpendicular of the triangle .​

Answer 1

Answer:

We can see that 4x+1 is the term with maximum value, i.e., hypotenuse, because it is already given that x>0. So, by using the property of a right-angled triangle, i.e., (hypotenuse)^2 = (side 1)^2 + (side 2)^2, we have

(4x+1)^2 = (4x)^2 + (2x-1)^2

=> 16x^2+8x+1=16x^2 + 4x^2 - 4x + 1

=> 8x + 4x = 16x^2 + 4x^2 - 16x^2 +1 - 1

=> 12x=4x^2

=> x = 3 (just the sides are interchanged and by cancelling the factors of ‘x’ and 4)

Therefore, we obtained the value of x.

Now, we shall see how to obtain the area of the triangle:

By using the formula, area(A)=(1/2)*base*height, we can get the value of the area of the given triangle.

=> A=(1/2)*(2x-1)*(4x)

By substituting the value of x, we get

2x-1 = 5m and 4x = 12m (since the units given here is meters)

=> A = (1/2)*5*12

=> A = 30 square meters

Hence, the value of the triangle’s area is obtained!!!!!