Question

The ratio of the side length of Square A to the side length of Square B is 11:9 the area of Square A is 448 cm^2. What is the perimeter of square B?

Answer 1

`\text{Square}A\sim\text{Square}B\ in\ scale\ k,\ then\ \text{Area}A:\text{Area}B=k^2\\\\a,\ b-\text{the lenght of the sides of the squares}\\\\a:b=11:9\to A_A:A_B=\left((11)/(9)\right)^2\\\\A_A=448\ cm^2\\\\\text{Substitute}\\\\(448)/(A_B)=\left((11)/(9)\right)^2\\\\(448)/(A_B)=(121)/(81)\qquad|\text{cross multiply}\\\\121A_B=(448)(81)\qquad|:121\\\\A_B=((448)(81))/(121)\\\\A_B=b^2\to b^2=((448)(81))/(121)\to b=\sqrt{((448)(81))/(121)}`

`b=\sqrt{((64)(81)(7))/(121)}\\\\b=(√((64)(81)(7)))/(√(121))\\\\b=(√(64)\cdot√(81)\cdot\sqrt7)/(11)\\\\b=((8)(9)\sqrt7)/(11)\\\\b=(72\sqrt7)/(11)\\\\\text{The perimeter is}\ P_B=4b\to P_B=4\cdot(72\sqrt7)/(11)=(288\sqty7)/(11)\ cm`

`Used:\\\\√(ab)=√(a)\cdot√(b)\\\\\sqrt{(a)/(b)}=(√(a))/(√(b))`