Question

what is the length of the diagonal AG in the cuboid shown

Answer 1

AD = 8 cm (Given)

DC = 6 cm (Given)

AE = 2cm (Given)

ΔADC forms a right angle triangle

Find Length AC:

AC² = AD² + DC²

AC² = 8² + 6²

AC² = 64 + 36

AC² = 100

AC = √100

AC = 10 cm

ΔAEG forms a right angle triangle

Find AG:

AG² = AE² + AD²

AG² = 2² + 10²

AG² = 4 + 100

AG² = 104

AG = 2√26 cm or 10.2 cm

Answer: The length of the diagonal, AG, is 2√26 cm

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ALTERNATIVE METHOD:

$\text{Length of diagonal = } \sqrt{l^{2}+b^{2}+h^{2}}$

$\text{AG = } \sqrt{ (8)^{2}+(6)^{2}+(2)^{2} }$

$\text{AG = } 2\sqrt{26} \text { units}$

Answer: The length of the diagonal, AG, is 2√26 cm

Answer 2

$\huge{\bold{\boxed{\boxed{\color{red}{Answer:-}}}}}$

Given,length,l=8cm

Breadth,b=6cm

And ,Height,h=2cm

We know that length of diagonal of a Cuboid

=$\bold{\sqrt{l^{2}+b^{2}+h^{2}}}$

=$\sqrt{8^{2}+6^{2}+2^{2}}$

=$\sqrt{64+36+4}$

=$\sqrt{104}$

=$10.19\:cm$

❤hope it helps you ❤

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