Question

Find the area of the base of a box of height 4
lateral surface area 120 cm² if
it's breadth.
cm an
inch
it's length
9th is twice​

Answer 1

Step-by-step explanation:

Answer

Let l and b be the length and breadth of box.

Therefore,

l=2b

Height of box (h)=4cm

Lateral surface area of box =120cm

2

(Given)

As we know that,

Lateral surface area of cuboid =2h(l+b)

∴2×4(2b+b)=120

⇒3b=

8

120

⇒b=

3

15

=5cm

Therefore,

Length of box =l=2b=2×5=10cm

Therefore,

Area of base of box

=l×b

=10×5=50cm

2

Answer 2

Correct Question :

• find the area of the base of a box of height 4 cm and lateral surface area of 120 cm square if its length is twice its breadth

Answer :

• Area of base of box is 50cm²

Given :

• height is 4 cm
• lateral surface area is 120cm²

To find :

• Area of the base

Solution :

• let the length of the box be l
• let the breadth of the box be x

According to Question :

length is twice its breadth so ,

• length = 2b

As we know that ,

• Lateral surface area of cuboid = 2h(l + b)

where h is 4cm , l is 2b , lateral surface area of cuboid is 120cm²

⟼ Lateral surface area of cuboid = 2h(l + b)

⟼ 2 x 4(2b + b) = 120

⟼ 3b = 120/8

⟼ 3b = 15

⟼ b = 15/3

⟼ b = 5 cm

∴ Breadth is 5cm

• length of the box = 2b = 2(5) = 10cm

Now we have to find the area of base of box :

• Area of base of box = l × b

⟼ Area of base of box = 10 × 5

⟼ Area of base of box = 50 cm²

∴ Hence , Area of base of box is 50cm²