Prove 2(lb+bh+lh)=(l+b+h)^2-(l^2+b^2+h^2)
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Answer:
Hint: Assume l, b, and h as the length, breadth, and height of a 3 – dimensional shape. Consider each option one – by – one and draw their diagram with the labeling of their dimensions. Check these options and find the expression for their area and volume, whichever physical quantity is asked, to get the correct answer.
Complete step-by-step solution
Here, we have been provided with a formula: -
2(lb+bh+hl)" role="presentation" style="box-sizing: border-box; font-family: "Open Sans", sans-serif; -webkit-tap-highlight-color: rgba(255, 255, 255, 0); display: inline; font-style: normal; font-weight: normal; line-height: 49px; font-size: 16px; text-indent: 0px; text-align: center; text-transform: none; letter-spacing: normal; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; padding: 0px; margin: 0px; position: relative;">2(lb+bh+hl)2(lb+bh+hl)
and we have to determine the shape and the physical quantity (area, volume, etc) from the given options.
Now, let us assume l, b, and h as the length, breadth, and height of the required shape. Let us consider each option one – by – one.
(a) Area of cuboid
So, here we have to check if the provided formula is the formula for the area of cuboid or not. A cuboid is shown below: -
Step-by-step explanation:
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CBSEMathematicsGrade 9Surface Area of Cuboid
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2( lb+bh+hl) is formula of: -
(a) Area of cuboid
(b) Area of cube
(c) Volume of cuboid
(d) None of these
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Hint: Assume l, b, and h as the length, breadth, and height of a 3 – dimensional shape. Consider each option one – by – one and draw their diagram with the labeling of their dimensions. Check these options and find the expression for their area and volume, whichever physical quantity is asked, to get the correct answer.
Complete step-by-step solution
Here, we have been provided with a formula: -
2(lb+bh+hl)" role="presentation" style="box-sizing: border-box; font-family: "Open Sans", sans-serif; -webkit-tap-highlight-color: rgba(255, 255, 255, 0); display: inline; font-style: normal; font-weight: normal; line-height: 49px; font-size: 16px; text-indent: 0px; text-align: center; text-transform: none; letter-spacing: normal; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; padding: 0px; margin: 0px; position: relative;">2(lb+bh+hl)2(lb+bh+hl)
and we have to determine the shape and the physical quantity (area, volume, etc) from the given options.
Now, let us assume l, b, and h as the length, breadth, and height of the required shape. Let us consider each option one – by – one.
(a) Area of cuboid
So, here we have to check if the provided formula is the formula for the area of cuboid or not. A cuboid is shown below: -
A cuboid has 6 faces made up of 6 rectangles. Two rectangles have dimensions l, b; two have b, h, and two have h, l. So, the total area of a cuboid will be the total area of these 6 rectangles.
⇒" role="presentation" style="box-sizing: border-box; font-family: "Open Sans", sans-serif; -webkit-tap-highlight-color: rgba(255, 255, 255, 0); display: inline; font-style: normal; font-weight: normal; line-height: 49px; font-size: 16px; text-indent: 0px; text-align: center; text-transform: none; letter-spacing: normal; word-spacing: normal; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; padding: 0px; margin: 0px; position: relative;">⇒⇒
Area = Ar.(ABCD)+Ar.(EFGH)" role="presentation" style="box-sizing: border-box; font-family: "Open Sans", sans-serif; -webkit-tap-highlight-color: rgba(255, 255, 255, 0); display: inline; font-style: normal; font-weight: 400; line-height: 49px; font-size: 16px; text-indent: 0px; text-align: left; text-transform: none; letter-spacing: normal; word-spacing: 0px; overflow-wrap: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; padding: 0px; margin: 0px; color: rgb(51, 46, 43); font-variant-ligatures: normal; font-variant-caps: normal; orphans: 2; widows: 2; -webkit-text-stroke-width: 0px; background-color: rgb(255, 255, 255); text-decoration-thickness: initial; text-decoration-style: initial; text-decoration-color: initial; position: relative;">Ar.(ABCD)+Ar.(EFGH)Ar.(ABCD)+Ar.(EFGH) + Ar.(ADEH)+Ar.(BCFG)
A cube consists of 6 faces and all of them are squares. So, there cannot be three different dimensions for length, breadth, and height for a cube. Here, the area is the sum of the area of all 6
Answer:
Step-by-step explanation:
RHS
=> 2(lb+bh+lh)
=> 2lb + 2lh + 2bh (1)
LHS
=> l² + b² + h² + 2lh + 2bh + 2lb - l² - b² - h²
=> 2lb + 2lh + 2bh (2)
As (1) = (2)
=> LHS = RHS
hence proved