Question

5. The sum of the length of two adjacent sides of a parallelogram is 16 cm. If their difference is 2 cm, find the length of each of the sides of the parallelogram.
​

Answer 1

Answer:

search-icon-header

Search for questions & chapters

search-icon-image

Class 8

>>Maths

>>Mensuration

>>Area of General Quadrilateral

>>The length of two adjacent ...

Question

Bookmark

The length of two adjacent sides of a parallelogram are 17 cm and 12cm. one of its diagonals is 25 cm long. Find the area of the parallelogram. Also find the length of altitude from vertex to the side of length 12 cm.

Medium

Solution

verified

Verified by Toppr

Area of triangle =

s(s−a)(s−b)(s−c)

Area of parallelogram=2× Area of the triangle formed by the adjacent sides and the diagonal

Sides are 17cm,12cm,25cm

Semi perimeter(s)=

2

12+17+25

=

2

54

=27cm

Area =

27(27−12)(27−17)(27−25)

⇒A=

27⋅15⋅10⋅2

⇒A=

3×3×3×3×5×2×5×2

⇒A=3×3×5×2

⇒A=90cm

2

∴ Area of parallelogram =2(90)=180cm

2

.

Let the height of the parallelogram be h

Given base b=12cm

A=b×h

⇒180=12×h

⇒

12

180

=h

∴h=15cm

∴ Length of altitude =h=15cm.