Question

The length, breadth and height of a wooden box with a lid are 10 cm, 9 cm and 7 cm, respectively. the total inner surface of the closed box is 262 cm2. the thickness of the wood (in cm) is

Answer 1

hii ur ans is 446 because 2*(10*9+9*7+10*7)=2(90+63+70)=2*223=4446 . please mark as brainliest

Answer 2

Answer:

1 cm

Step-by-step explanation:

Let the thickness be x

Outer length = 10 cm

Outer breadth = 9 cm

Outer Height = 7 cm

Inner length = 10-2x cm

Inner breadth = 9-2x cm

Inner  Height = 7-2x cm

Total inner surface area = $2(lb+bh+hl)$

                                    = $2((10-2x)(9-2x)+(9-2x)(7-2x)+(7-2x)(10-2x))$  ---1

Now we are given that he total inner surface of the closed box is 262 sq.cm.

So,  $2((10-2x)(9-2x)+(9-2x)(7-2x)+(7-2x)(10-2x))=262$  

$20x^2+190x+446=262$  

General form of quadratic equation : $ax^2+bx+c=0$

Using quadratic formula : $x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$

$x=\frac{-190\pm\sqrt{190^2-4(20)(446)}}{2(20)}$

$x=\frac{19}{4}-\frac{\sqrt{\frac{1069}{5}}}{4},\frac{19}{4}+\frac{\sqrt{\frac{1069}{5}}}{4}$

$x=1.0945,8.40$

So, x ≈ 1 , 8

Substituting x = 8 in 1 we get area = 318 sq.cm

Substituting x = 1 we gwt area = 262 sq.cm

Hence the thickness is 1 cm.