The length, breadth and height of a rectangular solid are in the ratio 5:4:2.If the total surface area is 1216cm,find length ,breadth and height of the solid
Answers
Given :
- Ratio be length, breadth and height of a rectangular solid = 5 : 4 : 2
- Total surface area of a rectangular solid = 1216 cm²
To find :
- Breadth, b
- Length, l
- Height, h
According to the question,
Let,
- Length = 5x
- Breadth = 4x
- Height = 2x
Now,
➞ Total surface area = 2(lb + bh + hl)
Where,
- l = length
- b = breadth
- h = height
➞ 1216 cm² = 2(5x × 4x + 4x × 2x + 2x × 5x)
➞ 1216 cm² = 2(20x + 8x + 10x)
➞ 1216 cm² = 2(38x)
➞ 1216 cm² = 76x²
➞ 1216 ÷ 76 = x²
➞ √16 cm = x
➞ 4 cm = x
- So, the value of x is 4 cm.
★ Length :
➞ 5x
➞ 5(4 cm)
➞ 20 cm
★ Breadth :
➞ 4x
➞ 4(4 cm)
➞ 16 cm
★ Height :
➞ 2x
➞ 2(4 cm)
➞ 8 cm
So,
- Length = 20 cm
- Breath = 16 cm
- Height = 8 cm
Answer:
Given :-
- The length, breadth and height of a rectangle solid are in the ratio of 5:4:2.
- Total surface area of a rectangular solid is 1216 cm².
To Find :-
- What is the length, breadth and height of a rectangular solid.
Formula Used :-
✪ T.S.A of rectangle = 2(LB + BH + HL) ✪
where,
- T.S.A = Total surface area
- L = Length
- B = Breadth
- H = Height
Solution :-
Let, the length be 5x
Breadth be 4x
And, the height will be 2x
According to the question by using the formula we get,
⇒ 2{(5x × 4x) + (4x + 2x) + (2x + 5x)} = 1216
⇒ 2(20x + 8x + 10x) = 1216
⇒ 2(38x) = 1216
⇒ 2x × 38x = 1216
⇒ 76x² = 1216
⇒ x² = 1216/76
⇒ x² = 16
⇒ x = √16
➠ x = 4 cm
Hence, the required length, breadth and height are,
✧ Length = 5x = 5 × 4cm = 20 cm
✧ Breadth = 4x = 4 × 4 cm = 16 cm
✧ Height = 2x = 2 × 4 cm = 8 cm
∴ The length, breadth and height of a rectangular solid is 20 cm, 16 cm and 8 cm respectively.
Let's Verify :
↦ 2{(5x × 4x) + (4x + 2x) + (2x + 5x)} = 1216
Put x = 4 we get,
↦ 2{(20 × 16) + (16 × 8) + (8 × 20)} = 1216
↦ 2(320 + 128 + 160) = 1216
↦ 2(608) = 1216
↦ 1216 = 1216
➦ LHS = RHS
Hence, Verified ✔