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
[tex]h=\sqrt{4w^{2}} = \sqrt{2*2*w*w} \\\\\\h = 2w[/tex]
b) Area of triangle = [tex]\frac{1}{2}b*h[/tex]
[tex]=\dfrac{1}{2}*(w^{2}-1) *2w\\\\= (w^{2}-1)*w = w^{2}*w - 1*w\\\\=w^{3}-w[/tex]
c) w =2
Area of triangle = 3w = 3*2 = 6
