Question

The sum of lenght,breadth and hieght of a cuboid is 19cm.The longest rod of lenght 5 underroot 5cm can be placed in it.Find the SA of cuboid.

Answer 1

5$\sqrt{5}$
$\sqrt{ l^{2}+ b^{2} + h^{2} }$ = 5$\sqrt{5}$
$l^{2} + b^{2} + h^{2}$ = $(5\sqrt{5}cm) ^{2}$ = $125 cm^{2}$ ----------------(1)
l+b+h = 19cm
$(l+b+h)^{2} = (19cm)^2$
$l^{2}+b^2+h^2+2(lb+bh+hl) = 361 cm^2$
$125cm^2 + surface area = 361 cm^2$
Hence, surface area = $361 cm^2 - 125 cm^2 = 236 cm^2$
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Answer 2

L+b+h=19cm
Longest rod that can be kept is along diagonal. So,
root over (l^2+b^2+h^2)=5root5
Squaring both sides
l^2+b^2+h^2=125
Or,(l+b+h)power 2-2(lb+lh+bh)=125
Or,-2(lb+lh +bh) =125-(l+b+h)power 2
Or,-2(lb+lh +bh)=125-19power2
Or,-2(lb+lh +bh)=125-361
Or,multiplying by - 1
2(lb+bh+lh)=236
Total surface area =2(lb+lh+bh)
=236sq.cm.

Hope this help. I think u are telling about total surface area. So I have solve this. Mark as brainliest if it's good and click thanx..