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2. A rectangular field is 30 m by 40 m. What distanceis saved by walking diagonally across the field ?3. A man travels 7 km due north, then goes 3 km dueeast and then 3 km due south. How far is he fromhis starting point ?pythagoras theorem class:- 9 s Chands series |
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Answer» Answer: if the person walks along the length and breadth of the rectangle: he walks 30 + 40 = 70m the length of the diagonal is x then x² = 30² + 40² ⇒ x = 50 ⇒ if he walks diagonally he walks 50m if he walks diagonally he saves a distance of 70 - 50 = 20m Step-by-step explanation: Length = 30 m. Breadth = 40 m. ●Diagonal can be found by dividing the rectangle along the diagonal. This FORMS 2 congruent right angle triangles. ●According to Pythagorean theorem: In a right angle triangle, hypotenuse² = adjacent side² + opposite side². Here: ●diagonal is the hypotenuse. ●length is the adjacent side. ●breadth is the opposite side. ◎Let the diagonal be denoted by the VARIABLE x. So, x²=30²+40². x²=900+1600. x²=2500. x=√2500. x=50. ○ Therefore, the length of the diagonal is 50 m. When the person walks using the length and breadth of the rectangle he covers 30+40 = 70 m, but when he walks using the diagonal of the rectangle he covers 50 m only. So, he saves 70-50 = 20 m by WALKING diagonally across it. ●Hence, the person saves 20 METERS by walking diagonally across |
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