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. :)
