Aside of a square is 2 cm greater than one of the sides of a rectangle and 5 cm smaller than the other side of the rectangle. find the area of the square, if it is known that it is 50 cm2 smaller than the area of the rectangle.

  400 cm²

Step-by-step explanation:

Let s represent the length of the side of the square in cm. Then the rectangle dimensions are (s-2) and (s+5), and the relation given by the problem statement is ...

  s² = (s -2)(s +5) -50

  s² = s² +3s -60 . . . . . . eliminate parentheses

  3s = 60 . . . . . . . . . . . . add 60-s²

  60/3 = s = 20 . . . . . . . the side length of the square is 20 cm.

The area of the square is (20 cm)² = 400 cm².

Check

The dimensions of the rectangle are 18 cm by 25 cm, so its area is 450 cm². The area of the square is 50 cm² smaller than that, as required.

p ÷ r = tan(x)

step-by-step explanation:

given that there is a figure below shows a right triangle: a right triangle is shown with hypotenuse equal to q units and the length of the legs equal to p units and r units.

graph is missing so i will create the graph as per given information.

the angle between the legs having lengths p units and q units is y degrees. the angle between the legs having lengths r units and q units is x degrees.

now we need to find about what is p ÷ r equal to.

so we can use trigonometric ratio tan(x)=[altitude]/[base] to find the value of p ÷ r, because p is the altitude and r is the base.

p ÷ r=tan(x)

hence final answer is p ÷ r=tan(x).