Question

Length = 5m , Breadth = 10 m , TSA (Total surface area = 700m^2) , Find Height and LSA then (Lateral Surface area) . Formula for LSA of cuboid = 2h (l+b) , Formula for TSA of cuboid = 2 (lb+bh+hl)​

Answer 1

Step-by-step explanation:

So,

TSA=2(lb+bh+hl)

700=2(50+10h+5h)

now, 700= 100+20h+10h

600=30h

h=600/30

Therefore,h=20m

Now, LSA= 2h(l+b)

LSA=2(5+10)20

=40×15

Therefore, LSA=600m²

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Answer 2

Analysis→

Here we're given that the length of a rectangle is 5m and breadth is 20m. And its TSA(total surface area) is 700m². And we've to find the height of the rectangle and its LSA(lateral surface area). And we know that :

${\dashrightarrow{\bf{LSA\:of\:rectangle=2\big(l+b\big)h}}}$

${\dashrightarrow{\bf{TSA\:of\:rectangle=2\big(lb+bh+hl\big)}}}$

Given→

• Length of rectangle=5m
• Breadth of rectangle=10m
• TSA of rectangle=700m²

To Find→

Height and LSA of the rectangle.

Answer→

$\maltese$ First let's find the height of the rectangle form the given Total Surface Area.

$\implies\rm{TSA=2\big(lb+bh+hl\big)}$

$\implies\rm{700m^2=2\big(lb+bh+hl\big)}$

$\implies\rm{\big(lb+bh+hl\big)=\dfrac{700m^2}{2}}$

$\implies\rm{\big(lb+bh+hl\big)=\dfrac{\cancel{700m^2}}{\cancel{2}}}$

$\implies\rm{\big(lb+bh+hl\big)=350m^2}$

${\implies{\rm{\Big[\big(5m\times10m\big)+\big(10m\times h\big)+\big(5m\times h\big)\Big]=350m^2}}}$

$\implies\rm{\Big[50m^2+10h+5h\Big]=350m^2}$

$\implies\rm{15h=300m^2}$

$\implies\rm{h=\dfrac{300m^2}{15m}}$

$\implies\rm{h=\dfrac{\cancel{300m^2}}{\cancel{15m}}}$

$\implies\rm{h=20m}$

${\underline{\boxed{\implies{\bf{h=20m\checkmark}}}}}$

_________________________

$\maltese$ Now we've found the height of the rectangle, so let's find its Lateral Surface Area ahead »

$\implies\rm{LSA=2\big(l+b\big)h}$

$\implies\rm{LSA=2\big(5m+10m\big)20m}$

$\implies\rm{LSA=40m\big(15m\big)}$

$\implies\rm{LSA=600m^2}$

${\boxed{\boxed{\bf{\therefore LSA\:of\:rectangle=600m^2\checkmark}}}}$

☞ Hence the height of the rectangle is 20m and its Lateral Surface Area is 600m^2 which is the required answer.

HOPE IT HELPS.