Question

The lengths of the sides of a triangle are in the ratio 3:4:5 and its perimeter is 48 cm. Find its area.
A
if the perimeter of an equilateral triangle is 36 cm, calculate its area and height correct to one
cimal place.​

Answer 1

Answer:

I hope you understand this

Answer 2

TRIANGLES

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The lengths of the sides of a triangle are in the ratio 3:4:5 and its perimeter is 48 cm. Find its area.

$\implies \sf \large 3 \: : \: 4 \: : \: 5$

$\implies \sf \large 3 + 4 + 5 = 12$

$\implies \sf \large48 \div 12 = 4$

$\implies \sf \large 3(4) + 4(4) + 5(4) = 12(4)$

$\implies \sf \large 12 + 16 + 20 = 48$

Thus, the measure of each sides are 12cm, 16cm, and 20cm. Now find the area by using the Heron's Formula.

$\implies\sf \large s = \frac{a + b + c}{2}$

$\implies\sf \large A= \sqrt{s(s - a)(s - b)(s - c)}$

$\:$

$\implies\sf \large s = \frac{12 + 16 + 20}{2}$

$\implies\sf \large s = \frac{48}{2}$

$\implies\sf \large \therefore \: s = 24$

$\:$

$\implies\sf A= \sqrt{24(24 - 12)(24 - 16)(24 - 20)}$

$\implies\sf \large A= \sqrt{24(12)(8)(4)}$

$\implies\sf \large A= \sqrt{9216}$

$\implies\sf \large \therefore \: A= 96$

$\:$

Final Answer:

$\: \sf \huge \orange{96 {cm}^{2} }$

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if the perimeter of an equilateral triangle is 36 cm, calculate its area and height correct to one decimal place.

$\implies\sf \large P=3s$

$\implies\sf \large 36=3s$

$\implies\sf \large \frac{36}{3} = \frac{ \cancel3s}{ \cancel3}$

$\implies\sf \large \therefore \: s = 12$

$\:$

Find the area of equilateral triangle with the given of 12cm in sides.

$\implies\sf \large A= \frac{ \sqrt{3} }{4} \: {s}^{2}$

$\implies\sf \large A= \frac{ \sqrt{3} }{4} \: {12}^{2}$

$\implies\sf \large A= \frac{ \sqrt{3} }{4} \:( 144 )$

$\implies\sf \large A= \frac{144 \sqrt{3} }{4}$

$\implies\sf \large A= 36 \sqrt{3}$

$\implies\sf \large A \approx 36(1.7)$

$\implies\sf \large \therefore \: A \approx 61.2$

$\:$

Final Answer:

$\: \sf \huge \orange{61.2 {cm}^{2}}$

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