The middle line of the trapezoid is 20 cm and divides the area in the ratio of 7 to 9. The bases of the trapezoid
| September 27, 2021 | education
The middle line of the trapezoid is 20 cm and divides the area in the ratio of 7 to 9. The bases of the trapezoid are equal ….
Let’s build the height BH. Since KM is the middle line of the trapezoid, it divides the height BH in half. BО = OH = BН / 2.
The area of the trapezoid KBСM is equal to: Skvcm = (BC + KM) * ВO / 2.
The area of the trapezoid AKMD is equal to: Sкмд = (АD + КМ) * ВН / 2.
Then Skvcm / Sacmd = ((BC + KM) * VO / 2) / (AD + KM) * BH / 2 = (BC + KM) / (AD + KM) = 7/9.
(BC + 20) * 9 = (AD + 20) * 7.
9 * BC – 7 * AD = -40. (1)
(BC + AD) / 2 = 20.
ВС + АD = 40. (2)
Let’s solve the system of equations 1 and 2.
BC = 40 – AD.
360 – 9 * AD – 7 * AD = -40.
16 * AD = 400.
AD = 25 cm.
BC = 40 – 25 = 15 cm.
Answer: a = 15 cm, b = 25 cm.
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