Question

the volume of a rectangular solid is 576 cubic centimetre and the length of a diagonal is under root 244 CM if its thickness be 6 cm find its length and breadth​

Answer 1

Step-by-step explanation:

rectangular is a property in a plane. so yout solid should be referred to as either a rectangular prism or equivalently a cuboid.

the volume of such bodies can be visualised as a neat stack of unit cubes.

so if the body is on a table with the known sides(5 and 10) on the table, then the first layer will obviously take 50 bricks.

how many layers (h) of 50 are needed to use up 650 bricks.

in general, you can see that the formula for the volume is width x breadth xheight

Answer 2

Mensuration

The volume of cuboid is given as 576 cm³.

The length of diagonal of the cuboid is √244 cm.

Thickness of cuboid is 6cm.

Formula for volume of cuboid is $(length\times\ breadth \times height)$.

Formula for the diagonal of the cuboid is $\sqrt{length^{2}+ breadth^{2} +thickness^{2} }$.

On putting the values in the formula, we get,

$576=length \times \ breadth\times6\\\\\implies96= length\times breadth-----(i)$

$\sqrt{244} =\sqrt{length^{2}+ breadth^{2}+ 6^{2} }$

on squaring both sides, we get,

$244= length^2+breadth^2+36\\\\\implies 208= length^2+breadth^2\\\\\implies 208=(length+breadth)^{2}-2(length\times breadth)------------(ii)$

putting (i) in (ii), we get

$208=(length+breadth)^2-2\times96\\\\\implies 400=(length+breadth)^2\\\\\implies 20=length+breadth$

Hence feasible measure of length is 12 cm and that of breadth is 8 cm.