The bases of a rectangular trapezoid are 7 dm and 19 dm. The smaller side is 9 dm.

| April 9, 2021 | education

The bases of a rectangular trapezoid are 7 dm and 19 dm. The smaller side is 9 dm. Calculate the large side of the trapezoid.

The larger base of a rectangular trapezoid is equal to the sum of the lengths of the smaller base and the projection of the lateral inclined side onto the larger base. This means that the projection of the lateral side is equal to the difference in the lengths of the bases: 19 – 7 = 12 dm. The smaller lateral side, perpendicular to the bases, coincides with the height of the trapezoid, therefore, the height of this trapezoid is 9 dm.

From a right-angled triangle formed by the larger lateral side, its projection and the height of the trapezoid, according to the Pythagorean theorem, we find the lateral side:

b ^ 2 = 9 ^ 2 + 12 ^ 2 = 81 + 144 = 225;

b = √225 = 15 dm.



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