Question

The edges of a cuboid are in the ratio 2 : 2 : 3 and its surface is 160 sq.M. The longer side of the cuboid is:

Answer 1

Answer:

Step-by-step explanation:

Let the edge of the cuboid is x:

ratio of sides is 2x : 2x : 3x; {l*w*h}

Surface area = 2 (lw+wh+hl)

Putting the values of edges in this formula:

160 = 2 (2x*2x + 2x*3x + 3x*2x);

160 = 2(4$x^{2}$ + 6$x^{2}$ + 6$x^{2}$);

80 = (4+6+6) $x^{2}$;

80/16 = $x^{2}$;

5 = $x^{2}$;

x = 2.23;

Longer side = 2.23 * 3 = 6.70

Answer 2

Answer:

The edges of a cuboid are in the ratio 2 : 2 : 3 and its surface is 160 sq.M. The longer side of the cuboid is 3√5 = 6.708 m

Step-by-step explanation:

The edges of a cuboid are in the ratio 2 : 2 : 3

Let say sides are 2x , 2x & 3x m

Surface Area = 2 * (2x  * 2x   + 2x * 3x  + 2x * 3x)

=> Surface Area = 2 * ( 4x² + 6x² + 6x²)

=> Surface Area = 2 * ( 16x²)

=> Surface Area = 32x²

32x² = 160

=> x² = 5

=> x = √5

=> x = 2.236

Longer side = 3x = 3 * 2.236 = 6.708 m