isosceles trapezoid
with a perimeter of 52 meters; one base is 10 meters greater than the other base; the measure of each leg is 3 less than twice the base of the shorter base
if the shorter base is b, then we have
b + b+10 + 2(2b-3) = 52
Now just solve for b and then the other base and legs.
To find the lengths of the bases and legs of the isosceles trapezoid, let's create equations based on the given information.
Let's assume that the shorter base of the trapezoid has a length of "x" meters. This means the longer base has a length of "x + 10" meters.
According to the given information, each leg of the trapezoid is 3 less than twice the base of the shorter base. So, each leg has a length of "2x - 3" meters.
The perimeter of the trapezoid is the sum of all its sides. In this case, it is given as 52 meters. Let's create an equation for the perimeter:
Perimeter = shorter base + longer base + 2 * leg
52 = x + (x + 10) + 2 * (2x - 3)
Simplifying the equation:
52 = x + x + 10 + 4x - 6
52 = 6x + 4
Rearranging the equation:
6x = 52 - 4
6x = 48
x = 48 / 6
x = 8
Now we have found the value of x, which is the length of the shorter base. Substituting this value back into the equations, we can find the lengths of the longer base and the legs.
Length of shorter base = x = 8 meters
Length of longer base = x + 10 = 8 + 10 = 18 meters
Length of each leg = 2x - 3 = 2 * 8 - 3 = 13 meters
So, the lengths of the bases are 8 meters and 18 meters, and the lengths of the legs are 13 meters each.