Question

Given a rectangle with a side of 10m and a dialogue of 26m. Find the perimeter of the rectangle.

Answer 1

Hi!

So rectangles have 4 right angles and the diagonal allows the rectangle to make 2 right traingles. Now we need to find the longer length and that can be found using the pythagorean theorem.

a^2 + b^2 = c^2

you have the b side and the c side but not the a

a^2 + 10^2 = 26^2

a^2 + 100 = 676

Now subtract 100 from both sides

a^2 = 576

dont forget to square root

a = 24

now find the perimeter

24 + 24 + 10 + 10 = 68

The perimeter is 68!

Hope this helps!

Answer 2

To find the longer side, use the Pythagoream theroem. 26m is the hypotenuse.

Pythagoream theorem: a² + b² = c² or c² - a² = b², in which "c" is the hypotenuse, and a and b can be used interchangeably.

c = 26

a = 10

b = b

Plug into corresponding areas.

c² - a² = b²

(26)² - (10)² = b²

Simplify.

26 x 26 = 676

10 x 10 = 100

676 - 100 = b²

b² = 576

Isolate the b. Root both sides

√b² = √576

b = √576

Simplify the root

b = √576

b = 24

The longer side of the rectangle = 24 m

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To find the perimeter, use the 2l + 2w = P formula.

w = width = 10

l = length = 24

P = perimeter

2(24) + 2(10) = P

Simplify

48 + 20 = P

Add

68 = P

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68 meters is your perimeter

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hope this helps