The sides of the base of the rectangular parallelepiped are 1: 7, the lengths of the diagonals

| September 17, 2021 | education

The sides of the base of the rectangular parallelepiped are 1: 7, the lengths of the diagonals of the side faces are 13 cm and 37 cm. Find the area of the side surface.

Let the edge AB be equal to X cm, then, by condition, the edge AD = 7 * X, and the edge AA1 will be denoted by Y.

In a right-angled triangle АА1В, according to the Pythagorean theorem

A1B ^ 2 = X ^ 2 + Y ^ 2.

X ^ 2 + Y ^ 2 = 169. (1).

In a right-angled triangle AA1D, according to the Pythagorean theorem

A1D ^ 2 = 72 * X ^ 2 + Y ^ 2.

49 * X ^ 2 + Y ^ 2 = 1369. (2).

Let’s solve the system of equations 1 and 2 by the addition method.

Subtract equation 1 from equation 2.

49 * X ^ 2 + Y ^ 2 – X ^ 2 – Y ^ 2 = 1369 – 169.

48 * X ^ 2 = 1200.

X ^ 2 = 1200/48 = 25.

X = 5.

AB = 5 cm.

Then AD = 5 * 7 = 35 cm.

5 ^ 2 + Y ^ 2 = 169.

Y ^ 2 = 169 – 25 = 144.

Y = 12.

AA1 = 12 cm.

Let us determine the area of ​​the lateral surface.

Side = (2 * AB + 2 * AD) * AA1 = (2 * 5 + 2 * 35) * 12 = 960 cm2.

Answer: S side = 960 cm2.



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