If the area of Triangle T, sides 5,12, and 13 equals the area of rectangle R, width 3, then what is the perimeter of rectangle R?
your triangle is right-angled, since
3^2+5^2=13^2
so the area is 30
so rectangle R is length x width = 30
3length = 30
length = 10
so its perimeter is 2(10+3) = 26
Where did you get 3^2 from?
I really don't know, lol, must be senility
of course I meant
5^2 + 12^2 = 13^2
the rest is still correct.
Lol, okay. Thank you very much !
To find the perimeter of rectangle R, we first need to find its length.
Since the area of Triangle T is given as the same as the area of rectangle R, we can find the length of the rectangle by dividing the area of the rectangle by its width.
Let's calculate the area of Triangle T using the given side lengths using Heron's formula. Heron's formula states that the area of a triangle with side lengths a, b, and c is given by:
Area = √(s (s - a) (s - b) (s - c))
where s is the semiperimeter of the triangle, given by:
s = (a + b + c) / 2
For Triangle T with sides 5, 12, and 13:
s = (5 + 12 + 13) / 2 = 30 / 2 = 15
Area = √(15(15 - 5)(15 - 12)(15 - 13))
= √(15 * 10 * 3 * 2)
= √900
= 30
Now, since the area of Triangle T is equal to the area of rectangle R, which is given as the product of its length and width (3), we have:
Length of rectangle R = Area of rectangle R / Width of rectangle R
= 30 / 3
= 10
Now, we can calculate the perimeter of rectangle R using the formula:
Perimeter = 2 * (Length + Width)
For rectangle R, with length = 10 and width = 3:
Perimeter = 2 * (10 + 3)
= 2 * 13
= 26
Therefore, the perimeter of rectangle R is 26 units.