The side of the rectangle is 4: 5 to its diagonal and the other side is 30. Find the area of the rectangle.

Given:

rectangle ABCE,

AC – diagonal,

AB: AC = 4: 5;

BC = 30.

Find the area of a rectangle, that is, S ABCE -?

Decision:

Consider a right-angled triangle ABC. By

Then, by the Pythagorean theorem (the square of the hypotenuse is equal to the sum of the squares of the legs):

AB ^ 2 + BC ^ 2 = AC ^ 2;

16x ^ 2 + 30 ^ 2 = 25x ^ 2;

25x ^ 2 – 16x ^ 2 = 900;

x ^ 2 * (25 – 16) = 900;

x ^ 2 * 9 = 900;

x ^ 2 = 900: 9;

x ^ 2 = 100;

x = 10;

4 * 10 = 40 – side of the rectangle;

40 * 30 = 1200 units ^ 2 – the area of the rectangle.

Answer: 1200 units ^ 2.