Find the lengths of the parallel sides of a trapezium (US: trapezoid)
by Oshi
(Dubai)
Question
ABCD is a trapezium (US: trapezoid) of area 91cm
2. CD is parallel to AB and CD is longer than AB by 8cm. if the distance between AB and CD is 7cm, find the lengths of AB and CD.
Answer
STEP 1: We know that, the area is 91cm
2 and CD is longer than AB. If we let AB be
x, CD is will be
x+8. Hence, we will have:
STEP 2: Now, since the distance between AB and CD is 7cm, the height of the trapezium is 7cm. Hence:
STEP 3: To find the lengths of AB and CD, we need to find
x. To do so, we start with the formula for the
area of a trapezium:
Where
a and
b are the parallel sides of the trapezium and
h is its height.
STEP 4: So, to find
x, we substitute
a with
x,
b with
x+8,
h with
7 and
A with
91. This gives:
STEP 5: Now, we simplify the equation:
STEP 6: Notice that, to find
x, we need to remove 7. We can do so by dividing both sides of the equation with
7.
STEP 7: Now, we can find
x by adding
-4 to both sides of the equation.
STEP 8: With
x=9, we can easily find the lengths of AB and CD:
