Question

The area of a square photo frame is 256cm². Find the perimeter of the photo frame. Product of a number and its half is 72. Find the number.​

Answer 1

Question :

The area of a square photo frame is 256cm². Find the perimeter of the photo frame.

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Given :

• Area of square photo frame = 256cm²

To find :

• the perimeter of the photo frame

Solution :

⇒ Let's find the side.

Area = s²

Side = √256

        = 16 cm

⇒ Now, let's find the Perimeter.

Perimeter of Photo Frame = 4 × s

                                            = 4 × 16  

                                            = 64 cm

Therefore, the perimeter of the Photo Frame is 64 cm.

                           ___________________

Question :

Product of a number and its half is 72. Find the number.​

-----------

Given :

• product of a number and its half is 72

To find :

• the number

Solution :

Let the number be x.

(x) × (x/2) = 72

x²/2 = 72

x² = 72 × 2

x² = 144

x = √144

x = 12

Therefore, the number is 12.

Answer 2

$\underline{\underline{\sf{\maltese\:Question\::-}}}$

• The area of a square photo frame is 256cm². Find the perimeter of the photo frame ?

$\underline{\underline{\sf{\maltese\:Concept\::-}}}$

$\odot$ Here we have given that The Area Of The Photo Frame is 256cm². As we know that to find The Perimeter of square photo frame we need side of the square So firstly we will find out the side of the square photo frame.

$\odot$  After finding the side of the square photo frame we will find out the Perimeter of the square photo frame by substituting the given values in the formula ( Perimeter of the Square = 4 × side ).

$\underline{\underline{\sf{\maltese\:Given\::-}}}$

$\qquad\sf{:\implies\:The\: area\: of \:a\: square\: photo\: frame \:is \:256\:cm^{2}}$

$\underline{\underline{\sf{\maltese\:To\:find\::-}}}$

$\qquad\sf{:\implies\:The\: Perimeter\:of\:the\:square\:photo\:frame}$

$\underline{\underline{\sf{\maltese\:Formulas\::-}}}$

$\qquad\sf{:\implies\:Area\:of\:the\:square\:=\:(side)^{2}}$

$\qquad\sf{:\implies\:The\: Perimeter\:of\:the\:square\:=\:4\:\times\:s}$

$\underline{\underline{\sf{\maltese\:Solution\::-}}}$

$\bigstar$ Let us find out the side of the square photo frame by using formulae (  side = √Area )

$\qquad\sf{:\implies\:side\:=\:\sqrt{Area}}$

$\qquad\sf{:\implies\:Side\:=\:\sqrt{256} }$

$\qquad\sf{:\implies\:Side\:=\:16}$

• Hence the side of the square photo frame is 16cm.

$\bigstar$ Let us find out the perimeter of the square photo frame by using formulae (  Perimeter = 4 × side )

$\qquad\sf{:\implies\:The\: Perimeter\:of\:the\:square\:=\:4\:\times\:s}$

$\qquad\sf{:\implies\:The\: Perimeter\:of\:the\:square\:=\:4\:\times\:16}$

$\qquad\sf{:\implies\:The\: Perimeter\:of\:the\:square\:=\:64}$

• Hence the Perimeter of the square photo frame is 64cm.

⠀⠀⠀⠀━━━━━━━━━━━━━━━━━━━━━━━━━⠀

$\underline{\underline{\sf{\maltese\:Question\::-}}}$

• Product of a number and its half is 72. Find the number.​

$\underline{\underline{\sf{\maltese\:To\:find\::-}}}$

$\qquad\sf{:\implies\:The\: Number}$

$\underline{\underline{\sf{\maltese\:Given\::-}}}$

$\qquad\sf{:\implies\:Product \:of \:a \:number \:and \:its\: half \:is \:72}$

$\underline{\underline{\sf{\maltese\:Solution\::-}}}$

$\bigstar$ Let the number be x

$\qquad\sf{:\implies\:(x)\:\times\:\dfrac{x}{2}\:=\:72}$

$\qquad\sf{:\implies\:\dfrac{x^{2}}{2}\:=\:72}$

$\qquad\sf{:\implies\:x^{2}\:=\:72\:\times\:2}$

$\qquad\sf{:\implies\:x^{2}\:=\:144}$

$\qquad\sf{:\implies\:x\:=\:\sqrt{144} }$

$\qquad\sf{:\implies\:x\:=\:12}$

• Hence the number is 12.