Question

the base of an isosceles triangle is 16 cm and its area is 48 cm^2. The perimeter of the triangle is -
A) 41
B)36
C)48
D)324
Answer it and explain!!!!!!

Answer 1

let hh be the perpendicular height from vertex to the base of length 16cm in given isosceles triangle then the area of isosceles triangle

12(16)(h)=4812(16)(h)=48

h=2×4816=6h=2×4816=6

Now, using Pythagorean theorem, each of equal sides of isosceles triangle is

=62+(162)2‾‾‾‾‾‾‾‾‾‾‾√=62+(162)2

=100‾‾‾‾√=100

=10 cm=10 cm

hence the perimeter of isosceles triangle

=sum of sides=sum of sides

=10+10+16=10+10+16

36cm

Answer 2

Question:

• The base of an isosceles triangle is 16 cm and its area is 48 cm^2. The perimeter of the triangle is?

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Given that,

• Base of an isosceles triangle is 16 cm. And, it's area is 48 cm².

☯ Let the Height be H cm.

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$\star\:\boxed{\sf{\pink{Area = \dfrac{1}{2} \times Height \times Base}}}$

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$:\implies\sf 48 = \dfrac{1}{\cancel{2}} \times H \times \cancel{16} \\\\\\:\implies\sf 48 = H \times 8 \\\\\\:\implies\sf H = \cancel\dfrac{48}{8} \\\\\\:\implies{\underline{\boxed{\sf{\pink{Height = 6 \: cm}}}}}\:\bigstar$

$\therefore\:{\underline{\sf{Hence, \ Height \ of \ \triangle \:is \ \bf{6 \ cm}.}}}$⠀⠀

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☯ Let the two equal sides be x cm.

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$:\implies\sf x = \sqrt{(8)^2 + (6)^2} \\\\\\:\implies\sf x = \sqrt{64 + 36}\\\\\\:\implies\sf x = \sqrt{100}\\\\\\:\implies{\underline{\boxed{\frak{\pink{x = 10 \ cm}}}}}\:\bigstar$

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» Now, finding perimeter of the triangle:

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$:\implies\sf Perimeter = 2 \times 10 + 16\\\\\\:\implies\sf Perimeter = 20 + 16\\\\\\:\implies{\underline{\boxed{\bf{\blue{Perimeter = 36 \: cm^2}}}}}\;\bigstar$

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$\therefore\:{\underline{\sf{Hence, \ perimeter \ of \ \triangle \ \:is \ \bf{Option \: b) \: 36 \ cm}.}}}$⠀⠀