Calculate the area of the triangle ABC shown in Figure 5 given that A = sqrt(s(s-a)(s-b)(s-c)) and S…

Question

Calculate the area of the triangle ABC shown in Figure 5 given that A = sqrt(s(s-a)(s-b)(s-c)) and S = (a+b+c)/2.

ScanSolve AI Tutor · Accepted Answer

Hapa kuna jinsi ya kukokotoa eneo la pembetatu ABC:

c) Calculate the area of the triangle ABC shown in Figure 5 given that $A = \sqrt{s(s-a)(s-b)(s-c)}$ and $s = \frac{a+b+c}{2}$ .

Tambua urefu wa pande za pembetatu.
Kutoka kwenye mchoro, tuna:
$a = 24$ cm (upande BC)
$b = 20$ cm (upande AC)
$c = 16$ cm (upande AB)
Kokotoa semi-perimeter $s$ .
$s = \frac{a+b+c}{2} = \frac{24 + 20 + 16}{2} = \frac{60}{2} = 30 \text{ cm}$
Kokotoa tofauti $(s-a)$ , $(s-b)$ , na $(s-c)$ .
$s-a = 30 - 24 = 6 \text{ cm}$ $s-b = 30 - 20 = 10 \text{ cm}$ $s-c = 30 - 16 = 14 \text{ cm}$
Badilisha maadili haya kwenye fomula ya Heron ili kukokotoa eneo $A$ .
$A = \sqrt{s(s-a)(s-b)(s-c)}$ $A = \sqrt{30 \times 6 \times 10 \times 14}$ $A = \sqrt{180 \times 140}$ $A = \sqrt{25200}$
Rahisisha mzizi wa mraba.
$A = \sqrt{3600 \times 7}$ $A = \sqrt{3600} \times \sqrt{7}$ $A = 60 \sqrt{7} \text{ cm}^2$
Jibu ni $60\sqrt{7} \text{ cm}^2$ .

Calculate the area of the triangle ABC shown in Figure 5 given that A = sqrt(s(s−a)(s−b)(s−c)) and S = (a+b+c)/2.