isosceles trapezoid with a perimeter of 52 yards the measure of one base is 10 yards greater than the other base the measure of each leg is 3 yards less than twice the length of the shorter base
To find the lengths of the bases and legs of the isosceles trapezoid, we need to set up equations based on the given information.
Let's assume that the shorter base has a length of x yards.
According to the information provided, the longer base is 10 yards greater than the shorter base, so its length is (x + 10) yards.
The legs of the trapezoid are each 3 yards less than twice the length of the shorter base, so their lengths are (2x - 3) yards.
The perimeter of a trapezoid is given by the formula P = a + b1 + b2 + c1 + c2, where P is the perimeter, a and c1 are the lengths of the legs, and b1 and b2 are the lengths of the bases.
Substituting the given values into the formula, we get:
52 = (2x - 3) + (x + 10) + (x + 10) + (2x - 3)
Simplifying the equation:
52 = 6x + 14
Now, isolate the variable by subtracting 14 from both sides:
38 = 6x
Divide both sides by 6 to solve for x:
x = 38/6
x = 6.333 approx.
So, the shorter base has a length of approximately 6.333 yards, and the longer base has a length of (6.333 + 10) = 16.333 approx. yards.
The length of each leg is 3 yards less than twice the length of the shorter base, which is (2 * 6.333 - 3) = 9.666 approx. yards.
Therefore, the lengths of the bases and legs of the isosceles trapezoid are approximately as follows:
Shorter base: 6.333 yards
Longer base: 16.333 yards
Legs: 9.666 yards