ABCD is an isosceles trapezoid. Segments BF and CE are both perpendicular to base AD. The ratio of AF to AD is 1:4. The perimeter of the triangle ABF is 24cm and the perimeter of the trapezoid ABCE is 48cm. If the perimeter of the rectangle BCEF is 40cm, find the perimeter of trapezoid ABCD
Solution
Let length of BC be x , then length of BF =20 -x
Let length of AF be y, then length of AD is 4y
now AB + 20-x +y =24--> AB = 4 + x-y
AB + x +20-x +x +y =48---> using tha above value of AB this eqn becomes x=12
AB 2 =(20-x) 2 + y 2 ----> (16-y) 2 =64+y 2 solving we get y= 6
so AB= 10,BC=12,AF=6,AD=24,EF=12 adding all these perimeter of ABCD= 64
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ABCD is an isosceles trapezoid- Segments BF and CE are both perpendicu (1).docx
1. ABCD is an isosceles trapezoid. Segments BF and CE are both perpendicular to base AD. The
ratio of AF to AD is 1:4. The perimeter of the triangle ABF is 24cm and the perimeter of the
trapezoid ABCE is 48cm. If the perimeter of the rectangle BCEF is 40cm, find the perimeter of
trapezoid ABCD
Solution
Let length of BC be x , then length of BF =20 -x
Let length of AF be y, then length of AD is 4y
now AB + 20-x +y =24--> AB = 4 + x-y
AB + x +20-x +x +y =48---> using tha above value of AB this eqn becomes x=12
AB 2
=(20-x) 2
+ y 2
----> (16-y) 2
=64+y 2
solving we get y= 6
so AB= 10,BC=12,AF=6,AD=24,EF=12 adding all these perimeter of ABCD= 64
