Question

Стороны параллелограмма равны 10 и 15см. Мельшая высота равна 8 см. Найдите большую высоту параллелограмма

Answer 1

Ответ:

$CF = 12$ cм.

Объяснение:

Обозначим данный параллелограмм буквами $ABCD.$

$AB = 15$ см.

$BC = 10$ см.

$AT = 8$ см.

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Меньшая высота параллелограмма проведена к большей стороне этого параллелограмма.

$\Rightarrow$ $AT$ опущена на сторону $CD.$

Тогда $CF$ опущена на сторону $></p> <p><img src=$ см и $AD = BC = 10$ см, по свойству параллелограмма.

$S _{ABCD} = AT \cdot CD = 8 \cdot 15 = 120$ см²

$S_{ABCD} = CF \cdot AD = CF \cdot 10 = 120$ см² $\Rightarrow CF = \frac{S_{ABCD}}{AD} = \frac{120}{10} = 12$ см.

Answer 2

To find the larger height of the parallelogram, we can use the formula for the area of a parallelogram, which is given by:

Area = base × height

Since we are given the smaller height and the lengths of the sides, we can find the area of the parallelogram using the smaller height, and then calculate the larger height using that area.

Let's denote the larger height as 'h' and the smaller height as 'h_s'. The area of the parallelogram is also given as:

Area = side1 × h_s

Given that side1 = 10 cm and h_s = 8 cm, we can calculate the area:

Area = 10 cm × 8 cm = 80 square centimeters

Now, we can use this area to find the larger height 'h' using the formula:

Area = side2 × h

Given that side2 = 15 cm, we have:

80 square centimeters = 15 cm × h

Now, we can solve for 'h':

h = 80 square centimeters / 15 cm ≈ 5.33 cm

So, the larger height of the parallelogram is approximately 5.33 centimeters.