SOLUTION: The diagonal of a rectangle is 25 ft. If the lenght of a rectangle is 15 ft. compute for the width, area and perimeter..

Question 534135: The diagonal of a rectangle is 25 ft. If the lenght of a rectangle is 15 ft. compute for the width, area and perimeter..
Answer by KMST(5328) (Show Source): You can put this solution on YOUR website!
The diagonal splits the rectangle into two right triangles.
In each of those right triangles,
the diagonal of the rectangle is the hypotenuse.
the length and width of the rectangle are the legs of the right triangle.
Their length are related according to Pythagoras theorem:
The sum of the squares of the lengths of the legs equals the square of the length of the hypotenuse.
If we call the length of the unknown side of the rectangle
or
and

The right triangles have legs (sides of the rectangle) of length 15 and 20.
I would say that the width of rectangle is 15 ft. and was given in the problem as "the length", while the longer side of the rectangle was computed as 20 ft. Was it meant as a trick question?
The area (in square feet) is

and the perimeter (in feet) is

MENTAL MATH NOTE: The right triangle involved in this problem has side lengths in the ratio 3-4-5. That set of numbers is the best loved and remembered "Pythagorean triple." Noticing from the start that the lengths given for the hypotenuse and one leg were in the ratio of 5 to 3, would allow you to calculate the length of the other side by mental math. Likewise, mental math tells you that a triangle with sides of length 3, 4,and 5 has a perimeter of 14 and two such triangles make a rectangle with an area of 12. Making all lengths 5 times larger would give a perimeter 5 times larger (70 ft) and an area 25 times larger (300 sq. ft.).
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