In the given figure, ∠ABC = 90° = ∠DEC, AC = 15 cm and AB = 9 cm. If the area of the quadrilateral ABCD is 72 cm2; find the length of DE.

ABC is a right angle triangle. Using Pythagoras theorem, ⇒ AC2 = AB2 + BC2 ⇒ BC2 = AC2 - AB2 = 152 - 92 = 225 - 81 = 144 ⇒ BC = = 12 As we know that area of triangle = x base x height Area of quadrilateral ABCD = Area of Δ ABC + Area of Δ BCD ⇒ 72 = x AB x BC + x BC x DE ⇒ 72 = x 9 x 12 + x 12 x DE ⇒ 72 = 9 x 6 + 6 x DE ⇒ 72 = 54 + 6 x DE ⇒ 6DE = 72 - 54 ⇒ 6DE = 18 ⇒ DE = ⇒ DE = 3 cm Hence, the value of DE = 3 cm.

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Mathematics

In the given figure, ∠ABC = 90° = ∠DEC, AC = 15 cm and AB = 9 cm. If the area of the quadrilateral ABCD is 72 cm²; find the length of DE.

Mensuration

Related Questions

If the difference between the two sides of a right-angled triangle is 2 cm and the area of the triangle is 24 cm²; find the perimeter of the triangle.

Calculate the area of quadrilateral ABCD in which ∠A = 90°, AB = 16 cm, AD = 12 cm and BC = CD = 12.5 cm.

How many square tiles of side 40 cm will be required to pave a footpath which is 2 m wide and surrounds a rectangular plot 80 m by 44 m ?

The cost of papering four walls of a room at ₹ 14 per square metre is ₹ 3,150. The height of the room is 5 metres. Find the length and the breadth of the room, if they are in the ratio 4 : 1.

Mathematics

In the given figure, ∠ABC = 90° = ∠DEC, AC = 15 cm and AB = 9 cm. If the area of the quadrilateral ABCD is 72 cm2; find the length of DE.

Mensuration

Related Questions

If the difference between the two sides of a right-angled triangle is 2 cm and the area of the triangle is 24 cm2; find the perimeter of the triangle.

Calculate the area of quadrilateral ABCD in which ∠A = 90°, AB = 16 cm, AD = 12 cm and BC = CD = 12.5 cm.

How many square tiles of side 40 cm will be required to pave a footpath which is 2 m wide and surrounds a rectangular plot 80 m by 44 m ?

The cost of papering four walls of a room at ₹ 14 per square metre is ₹ 3,150. The height of the room is 5 metres. Find the length and the breadth of the room, if they are in the ratio 4 : 1.

In the given figure, ∠ABC = 90° = ∠DEC, AC = 15 cm and AB = 9 cm. If the area of the quadrilateral ABCD is 72 cm²; find the length of DE.

If the difference between the two sides of a right-angled triangle is 2 cm and the area of the triangle is 24 cm²; find the perimeter of the triangle.