# Find the lengths of the parallel sides of a trapezium (US: trapezoid)

by Oshi
(Dubai)

##### Question
ABCD is a trapezium (US: trapezoid) of area 91cm2. 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.

STEP 1:    We know that, the area is 91cm2 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:

### Comments for Find the lengths of the parallel sides of a trapezium (US: trapezoid)

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 May 18, 2017 Rating goood NEW by: Anonymous gopootd

 Feb 26, 2017 Rating Doubt NEW by: Ayush In step 5 how you divided 7/2 with 2x and 8 there was only one 2 then how you divided 8 by it.

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 Feb 25, 2010 Rating trapezium by: oshi thankyou oshi

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