Find the missing length. Round to the nearest tenth, if necessary?

Question

http://gyazo.com/5d132e579583e490eb9f94264e12d022
Answers:
441
22.5
64
19.4

2. Use the rectangle below. Show all work.
a. Find the perimeter.
b. Find the area.

http://gyazo.com/f3c599b613c098bfc665acc665677e5e

I need help getting the answer step by step?

Answer 1

Recall: Pythagoras' theorem:

If c denotes the length of the hypotenuse and a and b denote the lengths of the other two sides, the Pythagorean theorem can be expressed as the Pythagorean equation is a² + b² = c²

Here a = 8, b = x and c = 21

So, 8² + x²  = 21²

64 + x² = 441

Subtract 64 from each side.

x² = 377

Take square root each side.

x = 19.4

Therefore answer is x = 19.4

Answer 2

Pythagoras' theorem:If c denotes the length of the hypotenuse and a and b denote the lengths of the other two sides, the Pythagorean theorem can be expressed as the Pythagorean equation is a² + b² = c².

Here a = 12, b = x, and c = 15.

So, 12² + x²  = 15²

144 + x² = 225

Subtract 144 from each side.

x² = 81⇒x = 9.

Rectangle formula: Area of rectangle=b×h, Perimeter of rectangle=2b+2h  where b=breadth, h=height.

Area of Rectangle = 12×9 = 108 unit²

Perimeter of Rectangle = 2(12) + 2(9) = 24+18=42 unit.