Question

find the diagonal of a quadrilateral whose area is 300m². the length of perpendicular from the opposite vertices are 14cm and 16cm respectively.​

Answer 1

Answer:

here is the answer

Step-by-step explanation:

The perimeter P of a rectangle is given by the formula, P=2l+2w , where l is the length and w is the width of the rectangle.

The area A of a rectangle is given by the formula, A=lw , where l is the length and w is the width.

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Answer 2

Answer:

The diagonal value is calculated to be 2000m.

Step-by-step explanation:

In the question here we have been given that the following two heights of the given quadrilateral are 16 cm(0.16m)  and 14 cm(0.14m) respectively. Now we know that the quadrilateral also contains a diagonal whose length is to be calculated. As we also know that the four-sided quadrilateral can be divided into two triangles with the diagonal as its base and the two heights being its perpendicular heights. It can be observed in the figure also. Therefore in quadrilateral PQRS with PN and RM as the heights and QS as the diagonal we have,

Therefore adding the area of both of these triangles will be equal to the given area of the quadrilateral which is 300$m^{2}$

Area of the quadrilateral = $\frac{1}{2} PN * QS + \frac{1}{2} RM * QS$

⇒ 300 = $\frac{1}{2}*0.14*QS + \frac{1}{2} *0.16*QS$

⇒ 300 = 0.07QS + 0.08QS

⇒ 300 = 0.15QS

⇒ QS = 2000m

Therefore the diagonal is 2000m.