Question

Two adjacent sides of parallelogram are 8 cm and 6 cm and its area is 48 cm^2. find the length of its diagonal by using area of scalene triangle​

Answer 1

The Diagonal Of The Parallelogram Is 6 Cm In Length

GIVEN

Length of one side of parallelogram = 8 cm

length of the adjacent side of the parallelogram= 6cm

Area of the parallelogram = 48 cm²

TO FIND

Length of the diagonal using area of a scalene triangle.

SOLUTION

We can simply solve the above problem as follows -

It is given that,

Length of one side of the parallelogram, A = 6 cm

Length of the adjacent side of the parallelogram, B= 8 cm

We know that,

A parallelogram is made up of two congruent scalene triangles.

If the parallelogram is ABCD with E as its diagonal

So, area of parallelogram = 2 × Area of the scalene triangle

Or,

$Area \: of \: the \: scalene \: triangle = \frac{area \: of \: parallelogram \: }{2} = \frac{48}{2}$

Area of the scalene triangle = 24 cm²

we know that,

$Area \: of \: a \: scalene \: triangle = \frac{1}{2} base \times height$

where,

base = 8 cm

height = diagonal of the parallelogram

putting the values in the above formula we get,

$24 = \frac{1}{2} \times 8 \times \: height$

$height = \frac{24}{4}$

Height = 6 cm

Hence, the diagonal of the parallelogram is 6 cm in length

#spj2