Find the perimeter and area.

P = 28

A = 48

Step-by-step explanation:

The perimeter of a rectangle is:

P = 2(w + l)

where P is the perimeter, w is the width, and l is the length.

The area of a rectangle is:

A = w · l

where A is the area, w is the width, and l is the length.

Both the equation for the area and the length of a rectangle requires both the width and the length. In the figure, only the width is given. The diagonal of the rectangle. The width, length, and the diagonal form a right triangle, so we can use the Pythagorean Theorem to find the length. Remember, the Pythagorean Theorem is:

a² + b² = c²

where a and b are the legs of the triangle and c is the hypotenuse.

The legs of the right triangle formed by the length, width, and diagonal are the length and the width, while the hypotenuse is the diagonal. Lets replace a with l (l = length), b with 6 (the width of the rectangle), and c with 10 (the length of the diagonal).

l² + 6² = 10²

Now solve for l.

l² + 6² = 10²

Simplify.

l² + 36 = 100

Subtract 36 from both sides to get rid of the +36 on the left side.

l² = 64

Take the square root of both sides to get rid of the ² on the left side.

√l² = √64

Simplify.

l = 8   (-8 is also a solution, but the length cannot be negative)

So now we know that the length is 8.

length = 8

width = 6

So now we have to find the perimeter (P) and the area (A). To do this, we can plug in 8 for l and 6 for w into the equations for the area and the perimeter.

P = 2(l + w)

  = 2(8 + 6)

  = 2(14)

  = 28

So the perimeter is 28.

A = l · w

   = 8 · 6

   = 48

So the area is 48.

P = 28

A = 48

I hope you find this helpful. :)

P = 28

A = 48

Step-by-step explanation:

First cutting out the triangle from the rectangle

We will use pythagorean theorem to solve for b

c² = a² + b²

10² = 6² + b²

100 = 36 + b²

b² = 100 - 36

b² = 64

b = √64

b = 8

Perimeter of a rectangle = 2 ( l + w)

= 2 ( 6 + 8)

= 2 (14)

= 28

Area = l × w

= 8 × 6

= 48

Therefore P = 28; A = 48

44

step-by-step explanation: