Bissoy.com
Doctors Medicines MCQs Q&A

In the given figure, PQRS is a parallelogram, a length and a breadth of the parallelogram are 80 cm and 25 cm respectively. If h1 + h2 = 84 cm, where h1 & h2 are the perpendiculars on the length and breadth of the parallelogram, then find the area of the parallelogram.

In the given figure, PQRS is a parallelogram, a length and a breadth of the parallelogram are 80 cm and 25 cm respectively. If h1 + h2 = 84 cm, where h1 & h2 are the perpendiculars on the length and breadth of the parallelogram, then find the area of the parallelogram. Correct Answer 1600 cm<span style="position: relative; line-height: 0; vertical-align: baseline; top: -0.5em;font-size:10.5px;">2</span>

Given:

PQRS is a parallelogram,

Length = 80 cm & Breadth = 25 cm

h1 + h2 = 84 cm, where h1 & h2 are the perpendiculars on the length and breadth of the parallelogram.

Formula used:

Area of parallelogram = Base × Height

Calculations:

[ alt="F1 Himanshu Aggarwal Anil 09.12.20 D6" src="//storage.googleapis.com/tb-img/production/20/12/F1_Himanshu%20Aggarwal_Anil_09.12.20_D6.png" style="width: 253px; height: 149px;">

Area of parallelogram = Base × Height

⇒ PQ × h1 = PS × h2

⇒ 80 × h1 = 25 × h2

⇒ h1/h2 = 5/16

Let h1 & h2 be 5x & 16x respectively.

h1 + h2 = 84 cm

⇒ 5x + 16x = 84

⇒ x = 4

⇒ h1 = 5x 

⇒ h1 = 20 cm

⇒ h2 = 64 cm

Now,

Area of parallelogram = Base × Height

⇒ PQ × h1

⇒ 80 × 20

⇒ 1600

∴ The area of the parallelogram is 1600 cm2.

Related Questions

Consider the 5 × 5 matrix \[{\text{A}} = \left[ {\begin{array}{*{20}{c}} 1&2&3&4&5 \\ 5&1&2&3&4 \\ 4&5&1&2&3 \\ 3&4&5&1&2 \\ 2&3&4&5&1 \end{array}} \right
Select from the alternatives that combination of numbers, which will form a meaningful word if given letters are arranged accordingly. \(\begin{matrix} \ \ \ \text{A} & \rm R & \rm W & \rm L & \rm E & \rm K \\\ \downarrow & \downarrow & \downarrow & \downarrow & \downarrow & \downarrow \\\ \ \ 1 & 2 & 3 & 4 & 5 & 6 \end{matrix}\)
Let A be an m × n matrix and Ban n × m matrix. It is given that determinant ($$I$$m + AB) = determinant ($$I$$n + BA), where $$I$$k is the k × k identity matrix. Using the above property, the determinant of the matrix given below is
\[\left[ {\begin{array}{*{20}{c}} 2&1&1&1 \\ 1&2&1&1 \\ 1&1&2&1 \\ 1&1&1&2 \end{array}} \right
Eigen values of the matrix \[\left[ {\begin{array}{*{20}{c}} 0&1&0&0 \\ 1&0&0&0 \\ 0&0&0&{ - 2i} \\ 0&0&{2i}&0 \end{array}} \right
In parallelogram PQRS, ∠P = 45°, PR and QS are the diagonals of the parallelogram. The mid-point QR is O. OX and OY are perpendicular to PQ and QR respectively. If OX = 8 cm and OY = 12 cm, then what is the area of the parallelogram PQRS?
In a coded language “ADETP” is coded as “$&$&&” and “DTPQUV” is coded as “&&&&$&”? What is the code word for “&&$$&$”?
The following question has three statements. Study the question and the statements and decide which of the statement(s) is necessary to answer the question. The area of the parallelogram with base 15 cm is what percentage of the area of rectangle with length 20 cm? I) The height of the parallelogram is 20% less than the breadth of the rectangle. II) The height of the parallelogram is 60% of the length of the rectangle. III) The area of the rectangle is 66.67% more than the area of the parallelogram.
In the given figure, PQRS is a parallelogram in which ∠SPQ = 30° and area of the parallelogram is 76 cm2. If PQ ∶ PS is 9.5 ∶ 4, then find the ratio of numerical value of area and perimeter of the parallelogram.
A middle school mathematics teacher asks his students to construct a rectangle with length 7 cm and breadth 4 cm. As the students completed the task, he further instructs them: (i) increase the length and breadth by 2 cm each and draw to see what figure you get (ii) decrease the length and breadth by 2 cm and draw to see what figure you get (iii) increase the length by 1 cm and decrease the breadth by 1 cm. Can you predict the type of figure without draving? Which principle of Zoltan Dienes theory of mathematics learning is he using in the above activity?
Length of a rectangle PQRS is equal to the length of side AB of a triangle ABC. Height of triangle from base AB is 8 times to the breadth of rectangle PQRS. If the perimeter of rectangle is 100 cm and the area of a rectangle is 600 cm2, then what will be the area of triangle ABC?