RS Aggarwal Class 8 Math Seventeenth Chapter Construction Of Quadrilaterals Exercise 17B Solution
EXERCISE 17B
(1) Construct a parallelogram ABCD in which AB = 5.2 cm, BC = 4.7 cm and AC = 7.6 cm.
Steps of construction:
(i) Draw AB = 5.2 cm
(ii) With A as centre and radius 7.6 cm draw an arc.
(iii) With B as centre and radius 4.7 cm draw another arc, cutting the previous arc at C.
(iv) Join BC and AC.
(v) With C as centre and radius 5.2 cm draw another arc, cutting the previously drawn arc at D.
(vii) Join DA and DC.
Then, ABCD is the required parallelogram.
(2) Construct a parallelogram ABCD in which AB = 4.3 cm, AD = 4 cm and BD = 6.8 cm.
Steps of construction:
(i) Draw AB = 4.3 cm
(ii) With B as centre and radius 6.8 cm draw an arc. Name the point as D.
(iii) With A as centre and radius 4 cm draw another arc, cutting the previous arc at D.
(iv) Join AD and BD.
(v) With D as centre and radius 4.3 cm draw another arc, cutting the previously drawn arc at C.
(vii) Join BC and DC.
Then, ABCD is the required parallelogram.
(3) Construct a parallelogram PQRS in which QR = 6 cm, PQ = 4 cm and ∠PQR = 60o.
Steps of construction:
(i) Draw QR = 6 cm
(ii) With Q as the centre make a angle 60o.
(iii) With Q as the centre of radius 4 cm, draw an arc. Name the point P.
(iv) Join P and Q.
(v) With P as the centre of radius 6 cm, draw an arc. Name the point as S.
(vi) Join PS and RS.
Then, PQRS is the required parallelogram.
(4) Construct a parallelogram ABCD in which BC = 5 cm, ∠BCD = 120o and CD = 4.8 cm.
Steps of construction:
(i) Draw BC = 5 cm
(ii) With C as the centre make a angle 120o.
(iii) With C as the centre of radius 4.8 cm, draw an arc. Name the point D.
(iv) Join C and D.
(v) With D as the centre of radius 5 cm, draw an arc. Name the point as A.
(vi) Join AB and DA.
Then, ABCD is the required parallelogram.
(5) Construct a parallelogram, one of whose sides is 4.4 cm and whose diagonals are 5.6 cm and 7 cm. Measure the other side.
Steps of construction:
(i) Draw AB = 4.4 cm.
(ii) Draw BX ⊥ AB.
(iii) With A as the centre and radius 5.6 cm draw an arc, cutting BX at C.
(iv) Join AC.
(v) With B as the centre and radius 7 cm, draw an arc. Name the point as D.
(vi) Join CD and AD.
Then, ABCD is the required parallelogram. The other side is 4.4 length.
(6) Construct a parallelogram ABCD in which AB = 6.5 cm, AC = 3.4 cm and altitude AL from A is 2.5 cm. Draw the altitude from C and measure it.
Steps of construction:
(i) Draw AB = 6.5 cm
(ii) Draw AX ⊥ AB. From point A, draw an arc of length 2.5 cm on the AX and the point as L.
(iii) Draw YZ ⊥ AX from point L.
(iv) Cut an arc of length 3.4 cm on the line YZ and name it as C.
(v) From point C, cut an arc of length 6.5 cm on the line YZ. Bname the point as D.
(vi) Join BC and AD.
Then, quadrilateral ABCD is a parallelogram.
The altitude from C measures 2.5 cm in length.
(7) Construct a parallelogram ABCD, in which diagonal AC = 3.8 cm, diagonal BD = 4.6 cm and the angle between AC and BD is 60o.
Steps of construction:
(i) Draw AC = 3.8 cm.
(ii) Bisect AC at O.
(iii) Make ∠COX = 60oand produce XO to Y.
(iv) Set off OB = ½ (4.6) cm = 2.3 cm and OD = ½ (4.6) cm = 2.3 cm, as shown.
(v) Join AB, BC, CD and DA.
Then, ABCD is the required parallelogram.
(8) Construct a rectangle ABCD whose adjacent sides are 11 cm and 8.5 cm.
Steps of construction:
(i) Draw AB = 11 cm.
(ii) Make 90o angle at A and B.
(iii) With A as the centre and radius 8.5 cm draw an arc. Name the point as D.
(iv) With B as the centre and radius 8.5 cm draw an arc. Name the point as C.
(v) Join AD and BC.
Then, ABCD is the required rectangle.
(9) Construct a square, each of whose sides measures 6.4 cm.
Steps of construction:
(i) Draw AB = 6.4 cm.
(ii) Make 90o angle at A and B.
(iii) With A as the centre and radius 6.4 cm draw an arc. Name the point as D.
(iv) With B as the centre and radius 6.4 cm draw an arc. Name the point as C.
(v) Join AD, CD and BC.
Then, ABCD is the required square.
(10) Construct a square, each of whose diagonals measures 5.8 cm.
Steps of construction:
(i) Draw AC = 5.8 cm.
(ii) Draw the right bisector XY of AC, meeting AC at O.
(iii) From O set OB = ½ (5.8) cm = 2.9 cm along OY and OD = 2.9 cm along OX.
(iv) Join AB, BC, CD and DA.
Then, ABCD is the required square.
(11) Construct a rectangle PQRS in which QR = 3.6 cm and diagonal PR = 6 cm. Measure the other side of the rectangle.
Steps of construction:
(i) Draw QR = 3.6 cm.
(ii) Draw QX ⊥ QR.
(iii) With R as the centre and radius 6 cm, draw an arc, cutting QX at P.
(iv) Join PR.
(v) With P as centre and radius 3.6 cm, draw an arc.
(vi) With R as the centre and radius equal to PQ draw another arc, cutting the previous arc at S.
(vii) Join PS and RS.
Then, ABCD is the required rectangle.
(12) Construct a rhombus the lengths of whose diagonals are 6 cm and 8 cm.
Steps of construction:
(i) Draw AC = 6 cm.
(ii) Draw a perpendicular bisector(XY) of AC, Which bisects AC at O.
(iii) OB = ½ (8) cm = 4 cm and OD = ½ (8) cm = 4 cm
(iv) Draw an arc of length 4 cm on OX and name that point as B.
(v) Draw an arc of length 4 cm on OY and name that point as D.
(vi) Join AB, BC, CD and AD.
Then, ABCD is the required rhombus.
(13) Construct a rhombus ABCD in which AB = 4 cm and diagonal AC is 6.5 cm.
Steps of construction:
(i) Draw AB = 4 cm.
(ii) With B as the centre, draw an arc of 4 cm.
(iii) With A as the centre, draw another arc of 6.5, cutting the previous arc at C.
(iv) Join AC and BC.
(v) With C as the centre, draw an arc of 4 cm.
(vi) With A as the centre, draw another arc of 4 cm, cutting the previous arc at D.
(vii) Join AD and CD.
Then, ABCD is the required rhombus.
(14) Draw a rhombus whose side is 7.2 cm and one angle is 60o.
Steps of construction:
(i) Draw AB = 7.2 cm
(ii) Make ∠ABY = 60o and ∠BAX = 120o
Sum of the adjacent angles is 180o
⇒ ∠BAX = 180o – 60o = 120o
(iii) Set off AD (7.2 cm) along AX and BC (7.2 cm) along BY.
(iv) Join C and D.
Then, ABCD is the required rhombus.
(15) Construct a trapezium ABCD in which AB = 6 cm, BC = 4 cm, CD = 3.2 cm, ∠B = 75o and DC ∥ AB.
Steps of construction:
(i) Draw AB = 6 cm
(ii) Make ∠ABX = 75o
(iii) With B as the centre, draw an arc at 4 cm. Name that point as C.
(iv) AB ∥ CD
∴ ∠ABX + ∠BCY = 180o
⇒ ∠BCY = 180o – 75o = 105o
(v) At C, draw an arc of length 3.2 cm.
(vi) Join A and D.
Then, ABCD is the required trapezium.
(16) Draw a trapezium ABCD in which AB ∥ DC, AB = 7 cm, BC = 5 cm, AD = 6.5 cm and ∠B = 60o.
Steps of construction:
(i) Draw AB = 7 cm
(ii) Make ∠ABX = 60o
(iii) With B as the centre, draw an arc of 5 cm. Name that point as C. Join B and C.
(iv) AB ∥ DC
∴ ∠ABX + ∠BCY = 180o
⇒ ∠BCY = 180o – 60o = 120o
(v) Draw ∠BC Y = 120o
(vi) With A as the centre, draw an arc of length 6.5 cm, which cuts CY. Mark that point as D.
(vii) Join A and D.
Then, ABCD is the required trapezium.
