The sum of the lengths of the bases of the trapezoid is 7 cm more than the height.

| March 4, 2021 | education

The sum of the lengths of the bases of the trapezoid is 7 cm more than the height. Find the height of the trapezoid if the area of the trapezoid is 114 cm2.

Let us denote the lengths of the bases of this trapezoid by a and b, and the height of this trapezoid by h.

According to the condition of the problem, the sum of the lengths of the bases of this trapezoid is 7 cm greater than its height, therefore, we can write the following ratio:

a + b = 7 + h.

It is also known that the area of ​​the trapezoid is 114 cm ^ 2, therefore, we can write the following ratio:

h * (a + b) / 2 = 114.

Substituting into the second ratio the value a + b = 7 + h from the first equation, we get:

h * (7 + h) / 2 = 114;

h ^ 2 + 7h = 228;

h ^ 2 + 7h – 228 = 0;

h = (-7 ± √ (49 + 4 * 228)) / 2 = (-7 ± √ (49 + 912)) / 2 = (-7 ± √961) / 2 = (-7 ± 31) / 2 ;

h1 = (-7 – 31) / 2 = -38 / 2 = -19;

h2 = (-7 + 31) / 2 = 24/2 = 12.

Since the height of the trapezoid is positive, the value h = -19 is not suitable.

Therefore, the height of the trapezoid is 12 cm.

Answer: The height of the trapezoid is 12 cm.



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