Question

The length of the length of the two adjacent sides of parallelogram are 17 cm and 12 centimetre one of its sides is one of its diagonal is 25 metre long find the area of parallelogram also find the length of altitude on the side of length 12 centimetre

Answer 1

Answer:

area of parallelogram = 180 sq cm

altitude of parallelogram with base 12 is 15

Step-by-step explanation:

parallel sides are 12 cm & 17 cm

diagonal of parallelogram 25 cm

area of parallelogram is equal to sum of two triangle

this makes two triangle with equal area

area of 1st triangle with sides 12, 17 & 25

using herons formula

$s = \frac{a + b + c}{2} = \frac{12 + 17 + 25}{2} = \frac{54}{2} = 27 \\ area \: = \sqrt{s(s - a)(s - b)(s - c)} \\ = \sqrt{27 (27 - 12)(27 - 17)(27 - 25)} \\ = \sqrt{27 \times 15 \times 10 \times 2} \\ = \sqrt{3 \times 3 \times 3 \times 3 \times 5 \times 5 \times 2 \times 2} \\ = 3 \times 3 \times 5 \times 2 \\ = 90 {cm}^{2} \\ area \: of \: parallelogram \: = 2 \times 90 = 180$

area of parallelogram = b × h = 180

height of parallelogram corresponding to the base taken as 12 cm

$180 = 12 \times h \\ h = \frac{180}{12} \\ h = 15$

hope you get your answer