Question

PLEASE HELP... VERY URGENT... WILL GIVE BRAINLIEST!!!

Answer 1

Answer:

Step-by-step explanation:

a) Pythagorean theorem,

altitude² + base² = hypotenuse²

h²  + (w² - 1)² = (w² + 1)²

                    h² = (w² + 1)² - (w² - 1)²    

{Compare with (a + b)² - (a -b)² = 4ab where a =w² & b = 1}

                   h² = 4*w²*1

                   h² = 4w²

                   $h=\sqrt{4w^{2}} = \sqrt{2*2*w*w} \\\\\\h = 2w$

b) Area of triangle = $\frac{1}{2}b*h$

                               $=\dfrac{1}{2}*(w^{2}-1) *2w\\\\= (w^{2}-1)*w = w^{2}*w - 1*w\\\\=w^{3}-w$

c) w =2

Area of triangle = 3w = 3*2 = 6