Question

A field in the form of a parallelogram has an area of 432m find the length of its diagonal on which the perpendicular drawn from two vertices on either side of it are 12 m long.

Answer 1

Answer:

The length of diagonal is 36 m

Step-by-step explanation:

Given: A field in the form of a parallelogram has an area of 432 m².

We need to find the length of diagonal. Let length of diagonal be x m.

As we know a diagonal divides parallelogram into two triangles.

Please see the attachment for figure.

If we add the area of two triangles it would be equal to area of parallelogram.

Formula: Area of triangle = $\frac{1}{2}\times b\times h$

Calculation:

Area of triangle 1 + Area of triangle 2 = Area of parallelogram

$\frac{1}{2}\times x \times h_1+\frac{1}{2}\times x\times h_2=432$

$\frac{1}{2}\times x \times 12+\frac{1}{2}\times x\times 12=432$

$12x=432$

$x=36$ m

Hence, The length of diagonal is 36 m

Answer 2

Step-by-step explanation:

Area of triangle 1 + Area of triangle 2 = Area of parallelogram

\frac{1}{2}\times x \times h_1+\frac{1}{2}\times x\times h_2=432

2

1

×x×h

1

+

2

1

×x×h

2

=432

\frac{1}{2}\times x \times 12+\frac{1}{2}\times x\times 12=432

2

1

×x×12+

2

1

×x×12=432

12x=43212x=432

x=36x=36 m