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.

Answer
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:

trapezium with parallel sides of x and x+8

STEP 2: Now, since the distance between AB and CD is 7cm, the height of the trapezium is 7cm. Hence:

trapezium with the height 7cm

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:

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:
substituted value
STEP 5:    Now, we simplify the equation:
simplifying 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.
dividing both sides with 7

STEP 7:    Now, we can find x by adding -4 to both sides of the equation.

x is equals to 9
STEP 8:   With x=9, we can easily find the lengths of AB and CD:

AB is 9cm and CD is 17cm


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Jul 18, 2016
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Jan 17, 2011
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Feb 25, 2010
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trapezium
by: oshi

thankyou

oshi

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