Question

(a) A square has an area of 81 cm. What is the length of each side? cm (b) A square has a perimeter of 8 m. What is the length of each side?

Answer 1

The side length of the square with area of 81 cm² is :

↬ 9 cm

The side of the square with the perimeter of 8 m is :

↬ 2 m

Solution:

We're given the area of a square : 81 cm².

To find one of its sides, we need to take the square root of that.

So we have:

`\sf{Side\:length{\square}=√(81)} \\ \\ \sf{Side\:length\square=9}`

We know that if we take the square root of 81, we will get two solutions: 9 and -9; however we cannot use -9, because having a negative side length is impossible.

So the side length is 9 cm.

__________________________

To find the side length when given the perimeter, we divide it by 4, because the formula for a square's perimeter is P = 4a.

So if we rearrange that for a, we will get : a = P/4.

where a = side length

Solving,

• a = 8/2
• a = 4

Hence, the length of each side is 4 m.

Answer 2

Answers:

(a) 9 cm

(b) 2 cm

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Work shown for part (a)

A = s^2

s = sqrt(A)

s = sqrt(81)

s = 9

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Work shown for part (b)

P = 4s

s = P/4

s = 8/4

s = 2