Question

the length of adjacent sides of a parallelogram are 17cm and 12cm .one of its diagonal is 25cm long . find the area of the parallelogram and also find the altitude from the vertex on the side of length 12cm. ​

Answer 1

Step-by-step explanation:

Area of parallelogram is base *height

17*12=204cm.sq

Answer 2

Answer: 180 cm² , 15 cm

Step-by-step explanation:

The diagonal of a parallelogram divides it into two congruent triangles.

We can find the area of the triangle using Heron's Formula.

a = 12

b = 17

c = 25

s = 54\2 = 27

Area = $\sqrt{s(s-a)(s-b)(s-c)}$

         = $\sqrt{27(27 - 12)(27-17)(27-25)}$

         = $\sqrt{27 \times 15 \times 10 \times 2 }$

         = $\sqrt{(3 \times 3 \times 3) \times (5 \times 3) \times (2 \times 5) \times 2}$

          = $\sqrt{3^{2} \times 3^{2} \times 5^{2} \times 2^{2}}$

          = $3 \times 3 \times 5 \times 2 = 90cm^{2}$

Since both triangles are congruent,

    Area of Parallelogram = 2(Area of triangle)

                                            = 2(90)

                                            = 180 cm²

Second Part:

Area of parallelogram = base x height

∴ Height = $\frac{Area}{Base}$

Area = 180 cm²

Base = 12 cm

Height = $\frac{180}{12}  = 15 cm^{2}$