1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
Question

# Two adjacent sides of a parallelogram are 10 cm and 12 cm. If one diagonal of it is 16 cm long; find area of the parallelogram. Also, find distance between its shorter sides.

A
119.8 cm2;11.98 cm
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
B
119.9 cm2;11.20 cm
No worries! Weâ€˜ve got your back. Try BYJUâ€˜S free classes today!
C
117.6 cm2;10.28 cm
No worries! Weâ€˜ve got your back. Try BYJUâ€˜S free classes today!
D
120.8 cm2;15.98 cm
No worries! Weâ€˜ve got your back. Try BYJUâ€˜S free classes today!
Open in App
Solution

## The correct option is A 119.8 cm2;11.98 cmGiven, AB=12 cm, BC=10 cmBD is the diagonal of parallelogram ABCD.Also BD=16 cmWe know, △ABD≅△DCB [S−S−S Congruence]Also, area of parallelogram ABCD = Area of △ABD + Area of △DCB = 2 × Area of △ABD = 2√s(s−12)(s−10)(s−16)s=12+10+162 = 19Therefore, area of parallelogram ABCD= 2√19(19−12)(19−10)(19−16) = 2√3591 = 2(59.92) = 119.8 cm2Also, h is the distance of the two shorter sides.We know, area of parallelogram = base×height = BC×hTherefore, h=Area of parallelogram ABCDBC⇒h=119.810⇒h=11.98 cm

Suggest Corrections
0
Join BYJU'S Learning Program
Related Videos
Properties of Parallelograms
MATHEMATICS
Watch in App
Join BYJU'S Learning Program