If a parallelogram ,the length of whose sides are 11 cm and 13 cm, has one diagonal 20 cm long, - Maths - Areas of Parallelograms and Triangles

Question

If a parallelogram ,the length of whose sides are 11 cm and 13 cm,
has one diagonal 20 cm long, then what is the length of the other
diagonal

Anuradha Sharma · Accepted Answer

Here we will find the area of triangle ABC then double it and then
we will use area of parallelogram in terms of diagonal
<img alt="" src=
"https://s3mn%20mnimgs%20com/img/shared/ck-files/ck_5501cc1441aa1%20png"
style="width: 516px; height: 311px;">
Here using heron's formula, Area of traingle ABC, Area = ss-as-bs-cs = 11+13+202=22Area of traingle ABC=2222-1122-1322-20=66 cm2So area of parallelogram ABCD = 2×66=132 cm2Now area of parallelogram in terms of diagonal = 12AC×BD=132BD = 26420=13
2 cm

If a parallelogram ,the length of whose sides are 11 cm and 13 cm, has one diagonal 20 cm long, then what is the length of the other diagonal .