# Find the sides of a rectangular trapezoid if its area is 120 cm and height 8 cm.

Find the sides of a rectangular trapezoid if its area is 120 cm and height 8 cm. One of the bases is 6 cm larger than the other.

The area of ​​the trapezoid is equal to the product of its midline by the height:

S = m h.

Find the middle line:

m = S / h;

m = 120/8 = 15 cm.

Since one of the bases is 6 cm larger than the other, and the middle line is equal to their half-sum, then we express:

x is the length of the base of the aircraft;

x + 6 is the length of the AD base;

m = (BC + AD) / 2;

15 = (x + x + 6) / 2;

x + x + 6 = 15 2 = 30;

x + x = 30 – 6;

2x = 24;

x = 24/2 = 12;

BC = 12 cm;

AD = 12 + 6 = 18 cm.

Since the trapezoid is rectangular, the length of the smaller lateral side is equal to the length of the height.

Find the length of the greater lateral side AB.

Consider the triangle ABH formed by the height BH. The segment ВH is 6 cm, since this is the difference in the length of the bases of the rectangular trapezoid.

AB ^ 2 = BH ^ 2 + AH ^ 2;

AB ^ 2 = 8 ^ 2 + 6 ^ 2 = 64 + 36 = 100;

AB = √10 = 10 cm.

Answer: the bases of the trapezoid are 12 cm and 18 cm, its sides are 8 cm and 10 cm.

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