Question

lateral surface area of cuboid is 520 metre square if length is 14 metre and breadth and height are in ratio 6 is to 5 then find breadth and height of cuboid​

Answer 1

Answer:

breadth = 12m

height = 10m

Step-by-step explanation:

lateral surface area of cuboid = 2h(l + b) = 520

length = 14 m

ratio of breadth and height is 6:5

breadth = 6x

height = 5x

2 × 5x (14 + 6x) = 520

10x( 14 + 6x) = 520

$14x + 6 {x}^{2} = \frac{520}{10} \\ 2(7x + 3 {x}^{2} ) = 52 \\ 7x + 3 {x}^{2} = \frac{52}{2} = 26 \\ 3 {x}^{2} + 7x - 26 = 0 \\ 3 {x}^{2} - 6x + 13x - 26 = 0 \\ 3x(x - 2) + 13(x - 2) = 0 \\ (x - 2)(3x + 13) = 0 \\ x - 2 = 0 \: \: \: \: 3x + 13 = 0 \\ x = 2 \: \: \: \: \: \: \: x = - \frac{13}{3}$

we take the positive value of x

x = 2

breadth = 6x = 6 × 2 = 12 m

height = 5x = 5 × 2 = 10 m

hope you get your answer