the breadth of a rectangle is 5 cm and each of its diagonal measures 13 cm find the length
please explain step by step
Answers
the answer is 34cm
Step-by-step explanation:
Width of a rectangle = 5 cm
Diagonal of a rectangle = 13 cm
By Pythagoras Theorem,
Length of a rectangle = √(13² - 5²)
Or, Length of a rectangle = √(169 - 25)
Or, Length of a rectangle = √144
Or, Length of a rectangle = 12 cm
Perimeter of a rectangle = 2(12+5)
Or, Perimeter of a rectangle = 2×17
Or, Perimeter of a rectangle = 34 cm
Therefore, the perimeter of a rectangle = 34 cm
explanation: By definition, the angles of a rectangle are right. Therefore, drawing a diagonal creates two congruent right triangles. The diagonal of the rectangle is the hypotenuse of the right triangle. The sides of the rectangle are the legs of the right triangle. We can use the Pythagorean Theorem to find the unknown side of the right triangle, which is also the unknown length of the rectangle.