Question

Solve this for me please it would be very much appreciated

Answer 1

Answer:

x= 8

Step-by-step explanation:

Right angled triangle :

Use Pythagorean theorem,

Base² + altitude² = hypotenuse²

x² + ( 2x - 1)² = (2x +1)²

(2x + 1)² - (2x-1)²  -x² = 0

$\boxed{(a+b)^{2}-(a-b)^{2}=4ab}$       {here, a = 2x and b = 1}}

4*2x*1 - x²= 0

8x - x² = 0

x(8 - x) =0

x = 0  {Ignore}  or 8 - x= 0

                  -x = -8

                   x = 8

x = 8

Answer 2

Since it is a right angled triangle, the side opposite to the 90° angle is the hypotenuse.

Therefore H= 2x + 1

Let,
L= 2x - 1
B= x

According to Pythagoras’ theorem:

H^2 = L^2 + B^2
(2x + 1)^2 = (2x - 1)^2 + x^2
4x^2 + 4x + 1 = 4x^2 - 4x + 1 + x^2
4x = -4x + x^2 (Since, 4x^2 and 1 cancel each other)

x^2 - 8x = 0
x (x-8) = 0

Hence,
x=0 or x=8.

(P.S: maybe incorrect too)