Question

area of parallelogramis 30 cm^2. if the length of two adjacent sides are 6 cm and 10 cm respectively. find its diagonal​

Answer 1

Answer:

the long diagonal d=15.49 ( rounded to the nearest hundredth)

the shortest d=√136-120(cos 30)=5.663 ( rounded to the nearest hundredth)

Step-by-step explanation:

Area=height * base

30=h*6

h=30/6=5 cm

height=asinФ

sinФ=5/10=1/2 (Ф=30)

alternate angle=180

180-30=150 degrees

diagonal²=a^2+b^2-2abcos150

d²=10²+6²-2(10)(6)(-√3/2)

d=√136+60(√3)

the long diagonal d=15.49 ( rounded to the nearest hundredth)

the shortest d=√136-120(cos30)=5.663