Question

The length , breadth and height of a cuboid are in the ratio 5:3:2. if the total surface area of the cuboid is 1550 cm². then find the measures of its edges.​

Answer 1

Step-by-step explanation:

Let length of the cuboid = 5x

breadth of the cuboid = 3x

height of the cuboid = 2x

Surface area of cuboid = 1550 cm²

2(lb + lh + bh) = 1550 cm²

putting values

2(5x × 3x + 5x × 2x + 3x × 2x) = 1550 cm²

2(15x² + 10x² + 6x²) = 1550 cm²

2× 31x² = 1550 cm²

62 x² = 1550 cm²

x² = 1550/62

x² = 25

x = 5 cm

So length = 5x = 25 cm

breadth = 3x = 15 cm

height = 2x = 10 cm

Hope this will help you

Answer 2

Answer:

Solution:

Let the length be 5x cm

breadth be 3x cm

height be 2x cm

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$\bf\blue{Then,}$

$\bf\pink{Surface\:area = 2(lb + bh + hl)}$

$\bf\red{Surface\:area = 2(5x.3x + 3x.2x + 2x.5x)}$

$\bf\purple{\implies 2(15x^{2} + 6x^{2} + 10x^{2})}$

$\bf\green{\implies 2 \times 31x^{2} }$

$\bf\orange{\implies 61x^{2} }$

Given,

$\bf{\implies 61x^{2}=1550 cm^{2} }$

$\bf{\implies x^{2}= \frac{1550}{62}}$

$\bf{\implies x^{2}= 25}$

$\bf{\implies x= \sqrt{25} }$

$\bf\red{\implies x= 5 cm }$

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Hence,

Length of the cuboid = 5 × 5 = 25 cm

Breadth of the cuboid = 3 × 5 = 15 cm

Height of the Cuboid = 2 × 5 = 10 cm

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Hope it will be helpful :)