Question

The sum of length, breadth and height of a cuboid is 19 cm and its diagonal is 55–√5 cm. Its surface area is​

Answer 1

$\huge\sf\pink{Answer}$

☞ TSA of the figure is 236 cm²

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$\huge\sf\blue{Given}$

✭ Sum of height, breadth & length of a cuboid is 19 cm

✭ Length of its diagonal is 5√5 cm

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$\huge\sf\gray{To \:Find}$

◈ The surface area?

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$\huge\sf\purple{Steps}$

$\large\underline{\underline{\sf Correct \ Question}}$

The sum of the length, breadth and depth of a cuboid is 19 cm and its diagonal is 5√5 cm. Its surface area is?

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We know that the length of a diagonal of a cuboid is given by,

$\underline{\boxed{\sf Length_{diagonal} = \sqrt{l^2+b^2+h^2}}}$

➝ $\sf \sqrt{l^2+h^2+b^2} = (5\sqrt{5})^2$

➝ $\sf l^2+h^2+b^2 = 125 \:\:\: -eq(1)$

So now we know that,

➳ $\sf l+b+h = 19$

➳ $\sf l^2+b^2+h^2 = 19^2$ «« Squaring both sides »»

➳ $\sf l^2+b^2+h^2 = 361 \:\:\: -eq(2)$

TSA of cuboid is given by,

$\underline{\boxed{\sf TSA_{Cuboid} = 2(lb+bh+lh)}}$

We know that,

$\sf\bigg\lgroup (a+b+c)^2 = a^2+b^2+c^2+2(ab+bc+ca)\bigg\rgroup$

»» $\sf l^2+b^2+h^2+2(lb+bh+lh)$

»» $\sf 125+TSA = 361$

»» $\sf TSA = 361-125$

»» $\sf\orange{TSA = 236 \ cm^2}$

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