2. The surface area of a cuboid is 720 m². Its length and breadth are in the ratio 4:3 and
height is 6 m. Find the:
(i) Length of the cuboid (ii) Breadth of the cuboid
Answers
Step-by-step explanation:
Given :-
TSA ᴏғ Cᴜʙᴏɪᴅ= 720 m²
Rᴀᴛɪᴏ of length and breadth = 4:3
Height = 6 m
To Find :-
(i) Length of the cuboid (ii) Breadth of the cuboid
Solution :-
Let,
Length = 4x
Breadth = 3x
We know that
TSA = 2(lb + bh + lh)
\begin{gathered}\sf TSA = 2(4x \times 3x + 3x \times 6 + 4x \times 6) \\ \end{gathered}
TSA=2(4x×3x+3x×6+4x×6)
\sf \red {720 = 2(12x^{2} + 18x + 24x)}720=2(12x
2
+18x+24x)
\tt \pink{ 720 = 2(12x^{2} +42x)}720=2(12x
2
+42x)
\sf \green{ 24x^{2} +84x - 720 = 024x }24x
2
+84x−720=024x
\sf \orange{ 2x^{2} +7x - 602x }2x
2
+7x−602x
\sf 2x^{2} - 8x + 15x - 60 = 02x2x
2
−8x+15x−60=02x
Taking x as common
\sf \red{ 2x(x - 4) + 15(x - 4) = 0}2x(x−4)+15(x−4)=0
\sf \green{(2x + 15),(x - 4)}(2x+15),(x−4)
Either
x = -15/2
or
x = 4
Since length can't be negative. So neglect the -15/2
{\textsf{\textbf{\orange{\underline{Length = 4(4) = 16 m}}}}}
Length = 4(4) = 16 m
{\textsf{\textbf{\pink{\underline{Breadth = 3(4) = 12 m}}}}}
Breadth = 3(4) = 12 m