Q8 of 99 Page 267

Pritha drew a parallelogram of which length of two diagonals are 6 cm and 8 cm and each angle between two diagonals is 90°. Let us write the length of sides of parallelogram and what type of parallelogram it is.


Given, AC ⊥ BD and ABCD is the parallelogram so its diagonals bisects each other at O


AO = OC = 4cm


BO = OD = 3cm


Now in Δ AOB


AO = 4cm


BO = 3cm


And ∠ AOB = 90° so its right angled triangle


And AB is the hypotenuse


AB2 = AO2 +OB2


⇒ AB =


⇒ AB =


⇒ AB = √ 25


⇒ AB =5 cm


Similarly, BC = DC = AD = 5cm


Since all the sides are equal and the diagonals bisects each other at 90°


⇒ the given parallelogram is a rhombus


More from this chapter

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6

Perimeter of any isosceles triangle is 544 cm. and length of each equal side is of length of base. Let us write by calculating the area of this triangle.

7

If the length of hypotenuse of an isosceles right-angled triangle is 12√2 cm. Let us write by calculating the area of this triangle.

 9

The ratio of the length of sides of a triangular park of our village is 2:3:4; perimeter of park is 216 meter.

(i) Let us write by calculating the area of the park.


(ii) Let us write by calculating how long is to be walked from opposite vertex of longest side to that side straightly.

 10

The length of three sides of a triangular filed of village of Paholampur are 26 meter, 28 meter and 30 meter.

(i) Let us write by calculating what will be the cost of planting grass in the triangular field at the rate of Rs. 5 per sq. meter.


(ii) Let us write by calculating how much cost will be for fencing around three sides at the rate Rs. 18 per meter leaving a space 5 meter for constructing entrance gate of that triangular field.