The area of an isosceles trapezoid is 77 square inches, the height is 4 inches and the legs are 5 - Maths -

Question

The area of an isosceles trapezoid is 77 square inches, the height
is 4 inches and the legs are 5 inches long Find the lengths of the
bases

Manbar Singh · Accepted Answer

Let ABCD be the isosceles trapezoid in which AB∥DC
Now, AD = BC = 5 inchesNow, AL = BM = 4 inchesIn ∆ALD,     DL2 = AD2 - AL2   Pythagoras theorem⇒DL2 = 52 - 42 ⇒DL2 = 25 - 16⇒DL2 = 9⇒DL = 3 inchesSimilarly, we get MC = 3 inchesNow, ABML is a rectangle
So, AB = LM  Opposite sides of rectangle are equalLet AB = LM = x inchesNow, area of ABCD = 77 sq inches⇒12AB + DC×AL = 77⇒AB + DC ×AL = 154⇒x + 3 + x + 3 × 4 = 154⇒2x + 6× 4 = 154⇒8x + 24 = 154⇒8x = 130⇒x = 1308 = 16
25So, AB = 16
25 inchesand DC = 3 + 3 + 16
25 = 22 25 inches

The area of an isosceles trapezoid is 77 square inches, the height is 4 inches and the legs are 5 inches long. Find the lengths of the bases.