The hypotenuse of right triangle is 52 centimeters long. The difference between the other two sides is 28 centimeters.Find the missing sides. Use exact values.
Accepted Solution
A:
Answer:The length of the perpendicular = 20 meters The length of the base = 48 metersStep-by-step explanation:The hypotenuse of the triangle = 52 metersLet the Length of the perpendicular is = k metersSo, the length of the base = ( k + 28) mNow, by PYTHAGORAS THEOREM , in a right angled triangle:[tex](BASE)^{2} + (PERPENDICULAR)^{2} = (HYPOTENUSE)^{2}[/tex]⇒ Here, [tex](k)^{2} + (k +28) ^{2} = (52)^{2}[/tex]Also, by Algebraic Identity: [tex](a+b) ^{2} = a^{2} + b ^{2} + 2ab\\ \implies (k+28) ^{2} = k^{2} + (28) ^{2} + 2(28)(k)\\[/tex]So, the equation becomes:[tex](k)^{2} +k^{2} + (28) ^{2} + 2(28)(k) = (52)^{2}[/tex]or, [tex]2k^{2} + 784+ 56k = 2704\\\implies k^{2} + 28k - 960 = 0[/tex]or,[tex]k^{2} + 48k -20 k - 960 = 0[/tex]Solving the equation: ⇒ (k+48)(k-20) = 0 , or (k+48) = 0 , or (k-20) = 0or, either k = -48 , or k = 20As k is the length of the side, so k ≠ - 48, k = 20Hence, the length of the perpendicular = k = 20 metersand the length of the base is k + 28 = 48 meters