Question

the dimensions of rectangular box are in the ratio of 2:3:4 and the difference between thr cost of covering it with a cloth at the rate of ₹ 10 and ₹ 11 per meter square is ₹ 1300. find the dimensions of the box.​

Answer 1

Answer:

Given,

Ratio of Dimensions of a rectangular box is 2:3:4

Here, x be the common part

Therefore,

Length (L) = 4×x = 4x m

Breadth (B) = 3×x = 3x m

Height (H) = 2×x = 2x m

Total surface area (T.S.A) = 2×(LB+BH+HL)

= 2×(4x×3x+3x×2x+2x×4) sq. m

= 2×(12x^2+6x^2+8x^2) sq. m

= 2 × 26x^2 sq. m

= 52x^2 sq. m

A.T.Q,

52x^2×11 - 52x^2×10 = 1300

or, 572x^2 - 520x^2 = 1300

or, 52x^2 = 1300

or, x^2 = 1300/52

or, x^2 = 25

or, x = √25

or, x = 5

Therefore,

Dimension of the box are -

Length = 4x = 4×5 = 20 m

Breadth = 3x = 3×5 = 15 m

Height = 2x = 2×5 = 10 m

Answer :- Dimension of the box are 20m×15m×10m.