Question

the area of an isosceles trapezoid is 77 square inches , the height measure and the legs are 5 inches long . Find the lengths of the bases .

the answer is 16.25 inches and 22.25 inches . HOW ???​

Answer 1

Answer:

lengths of bases are 16.25 , 22.25 inches

The area of a trapezoid is 77 square inches, the height measures 4 inches and the legs are 5 inches long. Find the length of the bases.

arrangements are shown in figure,

we know, in isosceles trapezoid, its height and congruent side form a right angled triangle.

so, from ∆ADL,

5² = 4² + DL²

⇒DL = 3 inches.

similarly, MC = 3 inches.

now area of trapezium = 1/2 (sum of parallel sides) × height

⇒77 = 1/2 × (AB + DC) × 4

⇒77/2 = (AB + LM + 2 × 3inches )

⇒77/2 = (AB + AB + 6) [ because, AB = LM ]

⇒38.5 = 2AB + 6

⇒AB = 32.5/2 = 16.25 inches

then, DC = AB + 6 inches

= 16.25 + 6 = 22 inches

Answer 2

Answer:

Hope this attachments helps you