Answer:Step-by-step explanation:Q1. The longest side of right triangle is 13 cm. if one of the two sides is 5cm, find the length of third side?Answer: the third side of the right triangle can be calculated using a Pythagoras' Theorem which is stated as the square of length of hypotenuse is equal to the sum of the square of length of other two sides. According to Pythagoras' Theorem c2= a2 + b2 c is the hypotenuse because its opposite to the right angle and is the longest side (13 cm)a is one side of the right triangle (x cm)b is the other side of the right triangle (5cm) putting values in the Pythagoras theorema2 + b2 = c2 a2 = c2 - b2 a2 = 132 - 52 a2 = 169 – 25 a2 = 144a = 12 cm ……… so the length of the third side of tringle is 12 cmQ2. Find The perimeter of the rectangle having one side measuring 15 m and the diagonal is 17 m?Answer. We know that diagonal is the hypotenuse (17 m) and one side of the rectangle is 15 m. so According to Pythagoras' Theorem c2 = a2 + b2 see the figure number 1c = 17 m b= 15m a = xa2 = c2 - b2 a2 = 172 - 152 a2 = 289 – 225 a2 = 64a= 8 m so third side length is 8 m and its width because its smaller than the other side 15 m which is length so according to formula perimeter of rectangle is = 2 (L+ W) = 2(15+8)perimeter of rectangle is = 46 mQ3. A man goes 20 m due west and then 15 m due north. How far it from the starting point?Answer is 25 m. see the figure number 2 for explanation Q4. the length of two sides of a triangle are 12 cm and 15 cm? between what two measure should the length of third side falls?AnswerThe third side must be greater in length than the difference of two sides while smaller than the sum of other sides. So sum of 2 sides = 12+15= 27 mDifference between two sides = 15-12= 3 mSo the length of third side must lies between 3 and 27 Q.5 ∠pqr is isosceles triangle with PQ = QR, if angle ∠Q is 50°. find the other two angles?Answer .Isosceles triangle with 2 equal sides. The right answer is ∠P65° and ∠R65°. I explained it in the figure number 3 below Q6. the two interior opposite angles of exterior angle of triangle are 60 and 80 degrees. Find the measure of exterior angle?Answer.The sum of the interior angles of triangle is equal to exterior angle of triangle. So sum of the interior opposite angles is 60 + 40= 140°. Explanation is in the figure number 4