Question

Two adjacent sides of a parallelogram are in the ratio 4:9 . If the perimeter of the parallelogram is 52cm find the length of its side & area, if the altitude to the shorter side is 12cm

Answer 1

Let the sides 4x and 9x.

We know,

Perimeter of parallelogram

= 2 x sum of adjacent

ATQ

Perimeter of paralllelogram = 52cm

$= 2(4x + 9x) = 52 \\ = 13x = \frac{52}{2} \\ = 13x = 26 \\ = x = \frac{26}{13} \\ = x = 2cm$

Required Adjacent Side

One side

$= 4x \\ = 4(2) \\ = 8cm$

Another side

$= 9x \\ = 9(2) \\ = 18cm$

Clearly,

$8cm < 18cm$

Hence , 18cm is the larger

side or base of the

parallelogram.

Corresponding Altitude = 8cm

Area of parallelogram

$= (base \times area) \: square \: units \\ = (18 \times 8) {cm}^{2} \\ 144 {cm}^{2}$

$Hence \: \ , the \: \: area \: \: of parallelogram \ \</u><u>=</u><u>of 144 {cm}^{2}$

Answer 2

Answer:

195$cm^{2}$

Step-by-step explanation:

Perimeter of trapezium = 52cm

Perimeter = 2*Sum of adjacent sides

           52 = 2*(9x+4x)

           52 = 2*13x

       52/2 = 13x

      26/13 = x

             x = 2

∴ Adjacent sides

         4x=4*2                9x=9*2

             =8cm                   =18cm

$(Height of trapezium)^{2}$ = $(hypo)^{2}$-$(side)^{2}$

                                    =$(18-8)^{2}$-$(7)^{2}$

                                    =$(10^{2} )$-$(7)^{2}$

                                    =$\sqrt{100+144}$

                                    =$\sqrt{244}$

                                    =15.62

Area of trapezium = 1/2*h(a+b)

                              = 1/2*15(18+8)

                              = 7.5(26)

                              = 195$cm^{2}$