A rectangular plot has length 3x+5 m and width 10x−15 m. Its perimeter is 400 m. Find its area in hectares.

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ScanSolve AI Tutor · Accepted Answer

Hapa kuna suluhisho la swali la 13:

Ili kupata eneo la maji yanayozunguka duara dogo, tunahitaji kuhesabu eneo la duara kubwa na kutoa eneo la duara dogo.

Tafuta rediasi ya duara dogo.
Kipenyo cha duara dogo ni $28 \text{ cm}$ .
Rediasi ya duara dogo, $r = \frac{\text{kipenyo}}{2} = \frac{28 \text{ cm}}{2} = 14 \text{ cm}$ .
Hesabu eneo la duara dogo.
Eneo la duara dogo, $A_{ndogo} = \pi r^2$ .
$A_{ndogo} = 3.14 \times (14 \text{ cm})^2$ $A_{ndogo} = 3.14 \times 196 \text{ cm}^2$ $A_{ndogo} = 615.44 \text{ cm}^2$
Hesabu eneo la duara kubwa.
Rediasi ya duara kubwa, $R = 42 \text{ cm}$ .
Eneo la duara kubwa, $A_{kubwa} = \pi R^2$ .
$A_{kubwa} = 3.14 \times (42 \text{ cm})^2$ $A_{kubwa} = 3.14 \times 1764 \text{ cm}^2$ $A_{kubwa} = 5538.96 \text{ cm}^2$
Hesabu eneo la maji yanayozunguka duara dogo.
Eneo la maji = Eneo la duara kubwa - Eneo la duara dogo.
$A_{maji} = A_{kubwa} - A_{ndogo}$ $A_{maji} = 5538.96 \text{ cm}^2 - 615.44 \text{ cm}^2$ $A_{maji} = 4923.52 \text{ cm}^2$
Eneo la maji yanayozunguka duara dogo ni $\text{4923.52 cm}^2$ .

A rectangular plot has length 3x+5 m and width 10x-15 m. Its perimeter is 400 m. Find its area in hectares.