Find The Dimensions Of This Cuboid

The whole surface: $2(lw+lh+wh)= 214$

$(lw+lh+wh)= 107$

$42+h(l+w)= 107$

$h(l+w)= 65$

volume= 210

$lwh= 210$

$(42)h= 210$

$h= 5$

$5(l+w)= 65$

$l+w= 13$

$l= 13-w$

$lw= 42$

$(13-w).w=42$

$w^2-13w +42=0$

$(w-6)(w-7)= 0$

$w= 6$ or $w=7$

$l= 13-w$

$l= 7$ or $l=6$

So, the sums of length, width, and height is 6+7+5= 18

length = L

breadth = B

height = H

area of base = B * H

42 = B * H         .........................(i)

volume = B * H * L

210 = (B * L) * H

210 = 42 * H [ from (i)]

 H = 5

surface area = 2(L B + B H + H*L)

  214  =  2(42 + 5B + 5L)

  5B + 5L + 42 = 107

  5(B + L) = 65

   B + L = 13

Therfore,

     H + B + L = 5 +13

                       =18

Let l represent the length, b represent the breadth and h represent the height of the cuboid.

Then we can derive the following equations based on the information provided.

1) lbh = 210

2) 2lb + 2lh + 2bh = 214

3) lb = 42

Afterwards, use simultaneous equations to find out the individual values of l,b and h. From equations 1 and 3, we can find h by this formula: h= lbh/lb = 210/42 = 5.

Then, from equation 2, we can simplify it to become lb + lh + bh =107, then substitute the value of h into the newly derived equation, which will become lb + 5l + 5b = 107.

Since lb = 42 from equation 3, we can safely conclude that 5l + 5b =107 -42 = 65.

Then factorize out the common factor 5 to get 5(l + b) = 65.

In the end, we should get l+b = 13. Then just add 13 to 5 to get 18, which is the sum of the lengths of the cuboid. Simple! :)

Let length = l Breadth=b Height=h. Total Surface area of a cuboid=2(lb+lh+bh). lb=42(given) So by substituting the value of lb in the equation of total surface area we get h(l+b)=65. We know lbh=Total volume=210(given) We know that h=65/(l+b). Therefore by subs. the value of h in volume formula we get l+b=13 therefore l+b+h=18.

2(lb + bh+ hl) = 214 ...... (1) lb = 42 ........(2) lbh = 210 ....... (3)

using (2) & (3), h = 5 substituting the values in (1), we get l + b = 13 so, l+b+h = 13 + 5 = 18

2(lb+bh+lh)=214 lb+bh+lh=214/2=107. Base area=lb=42. lb+bh+lh=107 bh+lh=107-42(lb=42) h(l+b)=65. Volume=lbh=210. volume/base area=lbh/lb=h h=210/42=5. h(l+b)=65 (l+b)5=65(h=5) l+b=65/5=13. l+b=13;h=5; l+b+h=13+5=18(Answer).

assume: l-length b-breadth h-height given lbh=210...............Eq.1 lb=42....................Eq.2 2(lb+bh+hl)=214.....Eq.3

eq.2/eq.1implies h=5 substitute h=5 in eq.3 that implies 2(42+5(l+b))=214 (l+b)=13 l+b+h=13+5=18

xy = 42 & xyz = 210 ==> z = 5 2xy + 2xz + 2yz = 214 <=> 2(42) + 10x + 10y = 214 <=> x + y = 13 <=> (42/y) + y = 13 <=> y^2 - 13y + 42 = 0 <=> x = 6 or 7 ==>y = 42/6 or 42/7 = 7 or 6 So (x+y+z) = 6+7+5 = 18 or (x+y+z) = 7+6+5 = 18

I solved it indirectly... I take volume and divide it by base area. I get 5. So, H = 5. Then I split base area as 6 x 7. Which is value nearer to height value. So, I take 5, 6, 7 as l,b,h. So, l+b+h = 18 :)

so simple man

whole surface area 2(ab+bc+ca)=214 area of base ab=42 Volume abc=210 42.c=210 c=5 ab+bc+ca=107 42+5(a+b)=107 on solving a+b+13 a+b+c=13+5 =18

the surface area is given in the formula 2lw+2lh+2wh=214 (1) the base area is lxw=42 cm²(2) and the volume is lxwxh= 210 cm3 since the base is l x w we can now get the height by dividing the volume (210) by the area of the base(42) 210cm3/42cm²=5cm=h substitute h in eq.1 2lw+2lh+2wh=214 2lw+10l+10w=214(3) now tAke the value of w from the second eq. w=42/l substitute it in eq. (3) 2l(42/l)+10l+10(42/l)=214 84+10l+420/l=214l 10l²-130l+420=0 divide by common factor w/c is ten then factor l²-13l+42=0 (l-6)(l-7) l=7 w=6 h=5 add up and it's 18

we know, volume = area of base * height 210 = 42 * h

h = 5 cm

Now, Total Surface Area = 214

2(lb + bh + lh) = 214

Substituting h = 5,

2(lb + 5b + 5l) = 214

lb + 5b + 5l = 214/2 = 107

Since base area = length * breadth = 42,

Substituting the value of lb = 42,

42 + 5(b + l) = 107

5(l+b) = 107-42 = 65

l+b = 65/5 = 13

Now we have l+b = 13

Add h=5 on both sides,

l+b+h = 13+h = 13+5 = 18cm

Answer = 18 cm

we have, 2(lb+bh+hl)=214 ........(1), l b h=210 ..............(2), l*b=42 ...(3) from (2) & (3) we get,
h=5.
put the value of h in ...(1). hence, we get (l+b)=13. so, l+b+h=18

Volume = $base area \times height$ . Height = $\frac{210}{42}$ = 5.

Surface area = 2(lb+lh+bh) = 214

lb+lh+bh = 107

But lb = 42... Therefore, lh+bh= 65.

But h = 5, therefore, 5(l+b)=65

l+b=13

Hence, l+b+h = 13+5 =18

First, equate lxw=42 which is the base area, then The total surface area which is 214= 2(lw+wh+lh) and the third equation is the volume 210=lxwxh. L=42/w 214= 2(lw+wh+lh) 107=lw+wh+lh 107=42/w(w)+wh+42/w(h) 65=wh+42/w(h) H=65w/w2+42 210=42/w(w)( 65w/w2+42) W2-13w+42=0 W=6 or 7 L=6 or 7 H=5 W+h+l=18

Let's say length, breadth and height are l,b,h resp. now, we have l b h=210 (volume of cuboid) l b =42 (base area of cuboid) substituting l b in above eq we get h=5; now total surface area of a cuboid is 2 (l b+b h+h l) = 214 (given) soving and subs known values we get sum =18

Let the length, breadth and height of the cuboid be $l,b,h$ respectively. We know that Area of Base $=lb$ , Volume of the cuboid $=lbh$ and Total Surface Area of Cuboid $=2(lb+bh+lh)$ .

GIven that, $lb=42 ...(i)$ and $lbh=210 ....(ii)$

Dividing (ii) by (i), we get, $\frac{lbh}{lb}=\frac{210}{42} \implies h=\boxed{5}$

So now we have the height, h=5 cm. Now, we have ---

$2(lb+bh+lh)=214$

$\implies 2(lb+h(l+b))=214$

$\implies 2(42+5(l+b))=214 \implies 84+10(l+b)=214 \implies 10(l+b)=130 \implies l+b=\boxed{13}$

So, Sum of $l,b,h = l+b+h = (l+b)+h = 13+5 = \boxed{18}$ cm

l,b,h.. 7,6,5 .... 18 do math

Let a,b and c be the length,breadth and height.

Its given ab=42 and abc=210, so c=5

Also given that 2(ab+bc+ca)=214

i.e ab+bc+ca=107

c(b+a)=65,since ab=42

a+b=13,c=5

So a+b+c=18

Let a,b,h be the length, breadth and height of the cuboid respectively. Thus from given Total surface area, 2(ab+bh+ha)=214 Base area, ab=42 Volume, abh=210

Solving we get, h=5 and a+b=13

thus, the required answer is 18

2 ( l x b ) + 2 ( h x b) + 2 ( l x h) = 214SqCm l x b = 42 SqCm & l x b x h= 210CuCm

Now the solution

42x h = 210 --- h = 210/42= 5Cm

2 x 42 + 2 x 5 b + 2 x 5 x l =214 10(l + b ) = 214- 84= 130 ( l + b ) = 13

Hence l +b+h= 13+5 = 18Cm