Question

an isosceles triangle has perimeter 24 cm and each of the equal side is 9 cm find the area of the triangle
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Answer 1

$\;\;\underline{\textbf{\textsf{ Given:-}}}$

• The length of the cuboid is 2 times of its breadth and 4 times of its height

$\;\;\underline{\textbf{\textsf{ To Find:-}}}$

• What's the total surface area of the cuboid?

$\;\;\underline{\textbf{\textsf{ Solution :-}}}$

Given that,

• The length is 2 times the breadth.

Then,

$\sf \longrightarrow l = 2b \\\\ \sf \longrightarrow b = \dfrac{l}{2}$

Again, it’s given that,

• The length is 4 times the height.

$\sf \longrightarrow l = 4h \\\\ \sf\longrightarrow h = \dfrac{l}{4}$

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$\bf\underline{\green{\:\:\:\:\:\:\:\:A.T.Q:-\:\:\:\:\:\:\:}}$

$\sf Volume \: of \: cuboid = 64m {}^{3} \\ \\ \longrightarrow \sf l \times h \times b = 64 {m}^{3} \\ \\ \longrightarrow \sf l \times \frac{l}{2} \times \frac{l}{4} = 64 {m}^{3} \\ \\ \sf \longrightarrow l {}^{3} = 64x8 {m}^{3} \\ \\ \sf \longrightarrow l {}^{3} = 4^{3} \times 2^{3} m ^{3} \\ \\ \sf \longrightarrow l ^{3} = ( {8m)}^{3} \\ \\ \sf \longrightarrow l = 8m$

$\underline{\textsf{ The length of the cuboid is \textbf{8 m }}}.$

Then, the breadth and height will be ___

$\sf h = \dfrac{8m}{2} \: \: and \: \: \: b = \dfrac{8m}{4} \\ \\ \sf \longrightarrow h = 4m \: \: and \: \: \longrightarrow b = 2m$

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Now , find the surface area.

$\sf S.A \: of \: cuboid = 2(8 \times 4+ 8 \times 2 + 4 \times 2) \\ \\ \sf \longrightarrow S.A \: of \: cuboid = 2(32 + 16 + 8) \\ \\ \sf \longrightarrow S.A \: of \: cuboid =2 \times 56 \\ \\ \sf \longrightarrow S.A \: of \: cuboid = 112m {}^{2}$

$\;\;\underline{\textbf{\textsf{ Hence-}}}$

$\underline{\textsf{ The required surface area of the cuboid is \textbf{ 112m²}}}.$

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$\;\;\underline{\textbf{\textsf{ Formula used :-}}}$

$\longrightarrow \: \: \sf Volume \: of \:cuboid = l \times h \times b \\ \longrightarrow \: \: \sf Surface \: area = 2(lh + lb + hb) \\ \sf where : \\ \sf l \longrightarrow \: length \: of \: cuboid \\ \sf h\longrightarrow \: \: height of \: cuboid \\ \sf b \longrightarrow breadth \: of \: cuboid$

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Answer 2

Answer:

Let the other side be x.

By question,

9+9+x=24

or, 18+x=24

or,. x=24-18

or, x=6 cm

Therefore the third side is 6 cm