Question

him guys plz tell me the answer fast...
two sides of a parallelogram are 10cm and 7cm.one of its diagonal is 13cm. find the area

Answer 1

Let ABCD be the parallelogram such thatAB=12cm;  BC=17cm  and  AC=25 cm.As the opposite sides of a parallelogram are equal, thenArea of triangle ABC=Area of triangle ADC The area of parallelogram ABCD= Area of triangle ABC+Area of triangle ADC=2×Area of triangle ABCUsing Herons formula, the area of triangle with sides a,b,c iss(s−a)(s−b)(s−c)−−−−−−−−−−−−−−−−√                        where s=a+b+c2Therefore, the area of triangle ABC=27(27−12)(27−17)(27−25)−−−−−−−−−−−−−−−−−−−−−−−√=90 cm2.Hence, the area of the quadrilateral ABCD=2×90 cm2=180 cm2.Now, let the length of the altitude from  vertex on the side of length 12cm, i.e. on AB be h.Then the area of the quadrilateral ABCD=AB×h                        [Area of quadrilateral=base×altitude]⇒12×h=90⇒h=9012=7.5cm.The required length of the altitude is 7.5cm.

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