Question

The base and the altitude of a parallelogram are in the ratio 3:2findthe measure of the base and altitude if the area of the parallelogram is 3750m

Answer 1

Answer:

base -- 75m

altitude -- 50m

Answer 2

⇒ Given:

The base and altitude of a parallelogram are in the ratio 3:2.

The area of the parallelogram is 3750 m².

⇒ To Find:

The measure of the length and the altitude.

⇒ Analysis

First we have to convert the ratio to two terms. Then we have to apply the formula to find the area of a parallelogram. Applying the required values in the formula, we will get the value of the variable and from that, we can derive the measures of the base and the altitude.

⇒ Formula to be used:

→ $\boxed{\sf{Area\:of\:a\:parallelogram=base\times\:height}}$

⇒ Solution:

Ratio of the base and altitude = 3:2.

Let the base be 3x and the altitude be 2x.

The given area of the parallelogram is 3750 m².

We know that:

Area of a parallelogram = base x height

That is,

3x x 2x = 3750 m²

6x² = 3750 m²

$\sf{x^2=\dfrac{3750}{6}}$

$\sf{x^2=625}$

$\sf{x=\sqrt{625}}$

$\sf{x=25}$

So, the value of x is 25.

Base of the parallelogram = 3x = 3 x 25 = 75 m

Height of the parallelogram = 2x = 2 x 25 = 50 m

Hence:

Base = 75 m

Height = 50 m

Parallelogram:

A parallelogram is a quadrilateral with the opposite pairs of sides and angles as equal and parallel.

$\setlength{\unitlength}{1 cm}\begin{picture}(0,0)\thicklines\qbezier(1,1)(1,1)(6,1)\put(0.4,0.5){\bf D}\qbezier(1,1)(1,1)(1.6,4)\put(6.2,0.5){\bf C}\qbezier(1.6,4)(1.6,4)(6.6,4)\put(1,4){\bf A}\qbezier(6,1)(6,1)(6.6,4)\put(6.9,3.8){\bf B}\end{picture}$

When the opposite pairs of angles of a parallelogram become 90°, it automatically forms a rectangle.