Question

The Length breadth and height of a rectangular solid are in the ratio 5:4:2 if the total surface area is 1216cm^2 find the Length breadth and height of the solid

Answer 1

let length breadth and height be 5x, 4x and 2x respectively.

Now, T.S.A of solid=2 (lb + bh +lh)
2 (5x × 4x+4x×2x +5x ×2x )=1216
2 (20x^2+8x^2+10x ^2)=1216
2×38x^2=1216
38x^2=1216/2
x^2=608/38
x^2=16
x=4
so,length =5×=5×4=20cm
breadth=4×=4×4=16cm
height=2×=2×4=8cm

Answer 2

Dear Student,

◆ Answer -

l = 20 cm

b = 16 cm

h = 8 cm

● Explanation -

Let x be some random variable such that -

l = 5x

b = 4x

h = 2x

Total surface area of the rectangular solid is -

TSA = 2 (lb + bh + lh)

1216 = 2 (5x×4x + 4x×2x + 5x×2x)

1216 / 2 = 20x^2 + 8x^2 + 10x^2

38x^2 = 608

x^2 = 16

x = 4

So now,

l = 5x = 5×4 = 20 cm

b = 4x = 4×4 = 16 cm

h = 2x = 2 × 4 = 8 cm

Thanks dear. Hope this helps you...