Question

In a parallelogram the base and the height are in the ratio 5:2. If the area of the parallelogram is \[360{{m}^{2}}\] , find its base and height.

Answer 1

Hint: Assume the ratio in x. The base and the height of the parallelogram are 5x and 2x respectively. We know the formula of area of the parallelogram, \[\text{Area = Base}\times \text{Height}\] . We have the area of the parallelogram which is equal to \[360{{m}^{2}}\] . Now, solve it further and get the value of x. Now, with the help of the value of x get the value of the base and height of the parallelogram.

Complete step-by-step answer:
According to the question, it is given that the area of the parallelogram is \[360{{m}^{2}}\] . The base and height of the parallelogram are in the ratio 5:2.
Let us assume the ratio be x.
The base of the parallelogram = 5x ………………..(1)
The height of the parallelogram = 2x ………………………..(2)

We know that the area of the parallelogram is the product of the base and height of the parallelogram. So,
\[\text{Area = Base}\times \text{Height}\] ………………….(3)
From equation (1) and equation we have the height and the base of the parallelogram.
Putting the value of the height and the base in equation (3), we get
\[\text{Area = (}5x)\times (2x)\]
\[\text{Area = }10{{x}^{2}}\] ……………….(4)
In the question, we have the area of the parallelogram which has area equal to \[360{{m}^{2}}\] .
\[\text{Area = }360{{m}^{2}}\] ……………………..(5)
On comparing equation (4) and equation (5), we get
\[\begin{align}
  & \text{ }10{{x}^{2}}\text{ = }360{{m}^{2}} \\
 & \Rightarrow {{x}^{2}}=36{{m}^{2}} \\
\end{align}\]
Taking square root on both LHS and RHS of the above equation, we get
\[\Rightarrow x=6m\] ………………….(6)
From equation (1) and equation (2), we have the base and height of the parallelogram in terms of x. So, we have to put the value of x in equation (1) and equation (2) to get the value of base and height of the parallelogram.
Now, putting the value of x in equation (1) and equation (2), we get
The base of the parallelogram = \[5(6)=30m\] .
The height of the parallelogram = \[2(6)=12m\] .
Hence, the height and the base of the parallelogram is 12 m and 12 m respectively.

Note:In this question, one might use the formula \[\text{Area =}\dfrac{1}{2}\times \text{Base}\times \text{Height}\] and then put the base as 5x and the height as 2x in this formula. This formula is wrong. This formula is used to calculate the area of the triangle not the parallelogram. The area of the parallelogram is, \[\text{Area = Base}\times \text{Height}\] . one must know all these formulas in order to solve any such questions.