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
Answers
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(lb+bh+hl)2(lb+bh+hl)
= 2((10−2x)(9−2x)+(9−2x)(7−2x)+(7−2x)(10−2x))2((10-2x)(9-2x)+(9-2x)(7-2x)+(7-2x)(10-2x))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))=2622((10-2x)(9-2x)+(9-2x)(7-2x)+(7-2x)(10-2x))=2622((10−2x)(9−2x)+(9−2x)(7−2x)+(7−2x)(10−2x))=262
20x2+190x+446=26220x^2+190x+446=26220x
2
+190x+446=262
General form of quadratic equation : ax2+bx+c=0ax^2+bx+c=0ax
2
+bx+c=0
Using quadratic formula : x=−b±b2−4ac2ax=\frac{-b\pm\sqrt{b^2-4ac}}{2a}x=
2a
−b±
b
2
−4ac
x=−190±1902−4(20)(446)2(20)x=\frac{-190\pm\sqrt{190^2-4(20)(446)}}{2(20)}x=
2(20)
−190±
190
2
−4(20)(446)
x=194−106954,194+106954x=\frac{19}{4}-\frac{\sqrt{\frac{1069}{5}}}{4},\frac{19}{4}+\frac{\sqrt{\frac{1069}{5}}}{4}x=
4
19
−
4
5
1069
,
4
19
+
4
5
1069
x=1.0945,8.40x=1.0945,8.40x=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.