Question

The ratio of length, breadth and height of a rectangular parallelopiped is 4:5:3 and its diagonal is 5root2. Find the area of its whole surface​

Answer 1

Solution

Given :-

• The ratio of length, breadth and height of a rectangular parallelopiped is 4:5:3
• Diagonal of rectangular parallelopiped = 5√2

Find :-

• Surface area of rectangular parallelopiped .

Explanation

We Have,

(The ratio of length, breadth and height of a rectangular parallelopiped is 4:5:3 )

Let,

• Length be(L) = 4x
• Breadth be(B) = 5x
• Height be(H) = 6x

Using Formula

$\boxed{\underline{\tt{\red{\:(Diagonal)^2\:=\:(Length)^2+(Breadth)^2+(Height)^2}}}}$

Keep all above Values,

==> ( 5√2)² = (4x)² + (5x)² + (3x)²

==> 5√2 × 5√2 = 16x² + 25x² + 9x²

==> 25 × 2 = 25x² + 25x²

==> 50x² = 50

==> x² = 50/50

==> x² = 1

==> x = 1

So,

• Length will be = 4 × 1 = 4 unit
• Breadth will be = 5 × 1 = 5 unit
• Height will be = 3 ×1 = 3 unit

Now, Calculate surface area

Using Formula

★ Surface area of rectangular parallelopiped = 2(LB + BH + HL)

Keep all above Values,

==> Surface area of rectangular parallelopiped = 2( 4×5 + 5×3 + 3×4)

==> Surface area of rectangular parallelopiped = 2( 20 + 15 + 12)

==> Surface area of rectangular parallelopiped = 2( 47)

==> Surface area of rectangular parallelopiped = 94 units³

Hence

• Surface area of rectangular parallelopiped will be = 94 units³

_____________________

Answer 2

Answer:

Total surface Area of rectangular parallelopopped is 60.16units

Step-by-step explanation:

A=2(wl+hl+hw)

w = 4x. l = 5x. h = 3x

diagonal

d = √[(4x)²+(5x)²+(3x)²] = 5√2

√(16x²+25x²36x²) = 5√2

√(77x²) = 5√2

squaring on both sides,

77x² = 50

x² = 50/77

x = 0.8

w = 4x = 4(0.8) = 3.2

l = 5x = 5(0.8) = 4

h = 3x = 3(0.8) = 2.4

Total surface area,

A=2(wl+hl+hw) = 2[(3.2)(4)+(2.4)(4)+(2.4)(3.2)]

= 2(12.8+9.6+7.68)

= 2(30.8) = 60.16