(www.tiwariacademy.net)
(Chapter – 12) (Heron’s Formula)(Exemplar Problems)
www.tiwariacademy.com
Question 7:
The dimensions of a rectangle ABCD are 51 cm × 25 cm. A trapezium PQCD
with its parallel sides QC and PD in the ratio 9:8, is cut off from the rectangle as
5
shown in the Fig. 12.6. If the area of the trapezium PQCD is th part of the area
6
of the rectangle, find the lengths QC and PD.
Answer 7:
We have dimensions of a rectangles ABCD as 51 cm and 25cm. Also, in
trapezium PQCD, parallel sides QC and PD are in the ratio: 9:8
i.e.,
QC:PD = 9:8
Let, length
QC = 9x
and
PD = 8x
According to the question,
𝐴𝑟𝑒𝑎 𝑜𝑓 𝑡𝑟𝑎𝑝𝑒𝑧𝑖𝑢𝑚𝑃𝑄𝐶𝐷 =
5
6
area of rectangle ABCD
1
(Sum of parallel Sides ) × distance between parallel sides
2
5
= × (BC × CD)
6
⇒
⇒
1
2
(8𝑥 + 9𝑥) × 25 =
5
6
× 51 × 25
1
A Free web support in Education
(www.tiwariacademy.net)
(Chapter – 12) (Heron’s Formula)(Exemplar Problems)
⇒
1
2
× 17𝑥 × 2 =
6
× 51 × 25
5 × 51 × 25 × 2
⇒
𝑥=
∴ Length,
𝑥 = 5
And
5
25 × 17 × 6
QC = 9 × 5 = 45cm
PD = 8 × 5 = 40 cm
2
A Free web support in Education