The area of a right triangle is 50. One of its angles is 45 degrees. Find the lengths of the sides and hypotenuse of the triangle.
Since it is a right triangle that means one of the angles is 90 deg. If another angle is 45 deg that means the remaining angle is also 45 deg Since you know that area for a triangle is 1/2*b*h and you know that the area is also 50 you can set those equal to each other 50 = 1/2 * b* h multiply both sides by 2 100 = b*h or 100/b = h Using law of sines A/sina = B/sinb = C/sinc h/sin(45) = b/sin 45 h = b 100/b = b 100 = b^2 b = 10 100/10 = h 10 = h So that gives you the height and the base which are the two sides of the triangle and then to find the hypotenuse we can use the pythagorean theorem 10^2 + 10^2 = hyp^2 100+100 = hyp^2 200 = hyp^2 Square root both sides to undo square and hypotenuse is approximately 14.14
(12x^2-32x)/(3x-8) First factor (4x(3x-8))/(3x-8) You can see that 3x-8 cancels so 4x is the simplification
(x-8)/5=2/4 Solve for x
(x-8)/5=2/4 First multiply both sides by 5 x-8=10/4 Add 8 to both sides x=10/4+32/4 (8 = 32/4) Then add x=42/4 Simplify x=21/2