Find the ratio of the areas of the squares PQRS to ABCD where PQ=9cm and AB=5cm?

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MrRoyal MrRoyal · Answer 1 · 2021-12-22T11:50:55+01:00

The area of a square is the square of its dimensions.

The ratio of the area of PQRS to ABCD is 25 : 81

The side lengths of the squares are given as:

[tex]PQ = 9cm[/tex] ----- square PQRS

[tex]AB= 5cm[/tex] --- square ABCD

The area of square PQRS is:

[tex]A_1 =PQ^2[/tex]

So, we have:

[tex]A_1 =(9cm)^2[/tex]

[tex]A_1 =81cm^2[/tex]

The area of square ABCD is:

[tex]A_2 =AB^2[/tex]

So, we have:

[tex]A_2 =(5cm)^2[/tex]

[tex]A_2 =25cm^2[/tex]

The ratio of the area of PQRS to ABCD is:

[tex]Ratio = A_2: A_1[/tex]

So, we have:

[tex]Ratio = 25cm^2: 81cm^2[/tex]

Cancel out the units

[tex]Ratio = 25: 81[/tex]

Hence, the ratio of the area of PQRS to ABCD is 25 : 81