One base of the trapezoid is 12 cm larger than the other. The middle line of the trapezoid is 14 cm.

| August 6, 2021 | education

One base of the trapezoid is 12 cm larger than the other. The middle line of the trapezoid is 14 cm. Calculate the larger base of the trapezoid.

Given:

ABCD – trapezoid.

ВС, АD – trapezoid bases.

ОS – the middle line of the trapezoid.

OS = 14 cm.

To find:

ВС, АD -? cm.

To solve this problem, we will use the theorem about the middle line of a trapezoid, according to which: the middle line of a trapezoid is parallel to the bases and is equal to their half-sum.

Thus, we get:

OS = (AD + BC): 2.

(AD + BC): 2 = 14.

Let the length of the BC base be x cm, then the AD base length is (x + 12) cm.

(x + (x + 12)): 2 = 14.

(x + x + 12): 2 = 14.

(2x + 12): 2 = 14.

2x + 12 = 14 x 2.

2x + 12 = 28.

2x = 28 – 12.

2x = 16.

x = 16: 2.

x = 8 (cm) – BC base length.

Then the length of the base АD is equal to: 8 + 12 = 20 (cm).

Answer: the length of the larger base of the trapezoid is 20 cm.



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