Math
posted by Beatrice .
The area of a trapezoid is 66 sq units. The length of its longer base is 4 units longer than the length of its shorter base, and its height is 7 units longer than the length of its shorter base. Find the length of each base and the height of the trapezoid.

you know that with bases b and c, and height h, a trapezoid has area
a = h * (b+c)/2
Just plug in your numbers, letting x be the length of the short base:
a = (x+7) * (x + x+4)/2
66 = (x+7)(x+2)
x^2 + 9x  52 = 0
(x+13)(x4) = 0
x = 4
short base = 4
long base = 8
height = 11
area = 11(8+4)/2 = 11*6 = 66
Respond to this Question
Similar Questions

Math
Abigail Adventuresome took a shortcut along the diagonal of a rectangular field and saved a distance equal to 1/3 the length of the longer side.Find the retio of the length of the shorter side of the rectangle to that of the longer … 
geometry
Two chords intersect a circle. The shorter chord is divided into segments of lengths of 9 inches and 12 inches. The longer chord has a length of 24 inches. Find the length of the shorter portion of the longer chord . 
Algebra
One base of trapezoid AGIE is four less than three times the other shorter base. The height of the trapezoid is one half of the shorter base. The area of the trapezoid is 210 square inches. Find the lengths of the bases and the height. 
Math
Write a simplified algebraic expression for the volume, V, of a rectangular prism that has a height 4 units longer than the length of the square base. evaluate the volume of x=10cm. 
math
One base of a trapezoid is twice as long as the other.the length of the shorter base is 9 cm and its height is 5 cm. What is its area? 
Algebra
The lenght of one base of a trapezoid is 19 less than five times the length of the other base. If the trapezoid has a height of 18 feet and an area of 477 ft2, find the length of the longer base 
algebra
The diagonal and the longer side of a rectangular plot are together three times the length of the shorter side. If the longer side exceeds the shorter side by 140 feet, what is the area of the plot? 
Math
A wire 32 cm long is cut into two pieces. The longer piece is 6 cm longer than the shorter piece. What is the length of the shorter piece? 
Math
A rectangular TV has an area of 1200 square inches. If the longer side is two inches longer than twice the shorter side, find the dimensions (length and height) of this flat screen TV 
geometry
The two nonparallel sides of an isosceles trapezoid are each 7 feet long. The longer of the two bases measures 22 feet long. The sum of the base angles is 140°. a. Find the length of the diagonal. b. Find the length of the shorter …