1.

in a triangle ABC;angle A=90degrees,side AB=xcm,AC=(x+5)cm and area =150cm2.find the sides of the triangle.

Answer»

ABC is a RIGHT TRIANGLE
Area of right triangle = 1/2 × base × HEIGHT
 
                                  = 1/2 × AB × AC
 
1/2 × (x) × (x+5) = 150

x(x+5) = 300

x² + 5x - 300 = 0

(x+20)(x-15) = 0

x = 15 

Sides AB = 15 cm and AC = 15 + 5 = 20 cm

Hypotenuse BC = \sqrt{20^2 + 15^2}

                          = \sqrt{400 + 225}

                          = \sqrt{625}

                          = 25


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