The length of two adjacent sides of a parallelogram are 17 cm and 12cm. one of its diagonals is 25 cm long. Find the area of the parallelogram. Also find the length of altitude from vertex to the side of length 12 cm.
The length of two adjacent sides of a parallelogram are 17 cm and 12cm. one of its diagonals is 25 cm long. Find the area of the parallelogram. Also find the length of altitude from vertex to the side of length 12 cm.
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Answer:
Area of triangle =
s(s−a)(s−b)(s−c)
Area of parallelogram=2× Area of triangle formed by the adjacent sides and the diagonal
Sides are 17cm,12cm,25cm
Semi perimeter(s)=
2
12+17+25
=
2
54
=27cm
Area =
27(27−12)(27−17)(27−25)
⇒A=
27⋅15⋅10⋅2
⇒A=
3×3×3×3×5×2×5×2
⇒A=3×3×5×2
⇒A=90cm
2
∴ Area of parallelogram =2(90)=180cm
2
.
h=?; b=12cm
A=b×h
⇒180=12×h
⇒
12
180
=h
∴h=20cm
∴ Length of altitude =h=20cm.
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Question
The length of two adjacent sides of a parallelogram are 17 cm and 12cm. one of its diagonals is 25 cm long. Find the area of the parallelogram. Also find the length of altitude from vertex to the side of length 12 cm
Solution
in△BCD:
Let
So,
→ s = (a + b + c)/2
→ (17 + 12 + 25)/2
→ 54/2
→ 27 cm
By heron's formula
Area of △BCD =
Now,
Area of parallelogram ABCD
→ 2 x Area of △BCD
→ 2 x 90
→
Also,
Therefore,
→ 180 = 12 x AE
→ AE = 180/12 = 15 cm
Hence