Ask Question
31 March, 20:48

The area of a rectangle is 16, and its diagonal is 68âˆ'âˆ'√. find its dimensions and perimeter.

+3
Answers (1)
  1. 31 March, 21:15
    0
    The perimeter of a rectangle is the sum of twice the length and twice the width. When a diagonal is drawn across the rectangle, two congruent triangles are formed. The legs of the triangle are the sides of the rectangle. Right triangles indicates that we can use the Pythagorean theorem. Let length = xLet width = y Set the equation based on what we know. 2x + 2y = 22 x + y = 11 eq1 x2 + y2 = [√65]2 eq2 We have two equations to work with. x + y = 11 eq1 x2 + y2 = 65 eq2 Substitute eq1 into eq2. From eq1, x = 11 - y x2 = (11 - y) 2 x2 = (11 - y) (11 - y) x2 = 121 - 22y + y2 (121 - 22y + y2) + y2 = 65 121 - 22y + 2y2 = 65 2y2 - 22y + 56 = 0 2 (y2 - 11y + 28) = 0 2 (y - 7) (y - 4) = 0 y = 7 and y = 4 Substitute these y values into eq1 to solve for x. x = 11 - 7 and x = 11 - 4 x = 4 and x = 7 Each pair of solutions has the same dimensions. Shorter side = 4Longer side = 7
Know the Answer?
Not Sure About the Answer?
Find an answer to your question 👍 “The area of a rectangle is 16, and its diagonal is 68âˆ'âˆ'√. find its dimensions and perimeter. ...” in 📗 Mathematics if the answers seem to be not correct or there’s no answer. Try a smart search to find answers to similar questions.
Search for Other Answers