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:


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: