SOLUTION: 7Kindly help me answer this problem. In isosceles trapezoid ABCD, the longer base, AB, is one and one half times as long as the shorter base, CD. The other two sides, AD and BC

Question 107082This question is from textbook Algebra Structure and Method
: 7Kindly help me answer this problem.
In isosceles trapezoid ABCD, the longer base, AB, is one and one half times as long as the shorter base, CD. The other two sides, AD and BC, are both 13 cm. long.
a. If the perimeter is 76 cm. find the lengths of AB and CD.
B. If the height of the trapezoid is 12 cm. find its area.
(Hint: Area= 1/2 x height x sum of base length) This question is from textbook Algebra Structure and Method

Answer by Annabelle1(69) (Show Source): You can put this solution on YOUR website!
draw a picture of the trapezium and label in the information we know. Let CD=x
So if CD=x, AB=1.5x and the other two sides are equal to 13.
An expression for the perimeter would be the sum of all four of these sides
P=x+1.5x +13+13
make this equal to 76
x+1.5x +13+13=76
2.5x+26=76
2.5x=76-26
2.5x=60
x=60/2.5
x=24
so cd= 24
cb=1.5x
=1.5*24
=36

Now for the area:
Area= 1/2 x height x sum of base length
height=12
sum of base lengths is 24+36=60
Area=0.5*12*60
=360cm^2
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