Question

Find the area of a triangle two sides of which are 18 cm and 10 cm and and perimeter 42cm

Answer 1

Answer:

third side of triangle=18+10-42 cm

=14

first side of triangle=18

second side of triangle=10

third side of triangle=14

area of triangle=18×14×10÷2

=1260 sqcm

Ans.=area of triangle which side is 18,14 and 10 is 1260 sqcm

Answer 2

Step-by-step explanation:

GivEn:

• Sides of triangle = 18 cm and 10 cm

• Perimeter of triangle = 42 cm

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To find:

• Area of triangle?

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Solution:

$\setlength{\unitlength}{1.5cm}\begin{picture}(6,2)\linethickness{0.4mm}\put(10.6,2.9){\large\sf{C}}\put(7.7,1){\large\sf{A}}\put(10.6,1){\large\sf{B}}\put(8,1){\line(1,0){2.5}}\put(10.5,1){\line(0,2){1.9}}\qbezier(8,1)(8.5,1.4)(10.5,2.9)\put(9,0.7){\sf{\large{18m}}}\put(10.7,1.9){\sf{\large{10 m}}}\put(10.3,1){\line(0,1){0.2}}\put(10.3,1.2){\line(3,0){0.2}}\put(8,1){\circle*{.15}}\put(7.3,2){\sf{\large{West}}}\put(11.7,2){\sf{\large{East}}}\put(10,0){\sf{\large{South}}}\put(10,3.8){\sf{\large{North}}}\end{picture}$

⠀

$\frak{Here} \begin{cases} & \sf{a = 18\;cm } \\ & \sf{b = 10\;cm } \\ & \sf{c = ?} \end{cases}$

We know that,

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✇ Perimeter of triangle = Sum of its all sides

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$:\implies\sf 42 = 18 + 10 + c$

$:\implies\sf 42 = 28 + c$

$:\implies\sf c = 42 - 28$

$:\implies\bf c = 14 cm$

Therefore, Third side of triangle is 14 cm.

⠀⠀━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━

Semi - perimeter, s = 42/2 = 21 cm

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✇ Now, Finding Area of triangle using Heron's Formula,

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$\star\;{\boxed{\sf{\purple{Area = \sqrt{s(s - a)(s - b)(s - c)}}}}}$

$:\implies\sf \sqrt{21(21 - 18)(21 - 10)(21 - 14)}$

$:\implies\sf \sqrt{21 \times 3 \times 11 \times 7}$

$:\implies\sf \sqrt{4851}$

$:\implies{\boxed{\frak{\pink{21 \sqrt{11}\;cm^2}}}}\;\bigstar$

$\therefore\;{\underline{\sf{Hence,\;Area\;of\;triangle\;is\; \bf{21 \sqrt{11}\;cm^2.}}}}$