Set 1Old McDonald has a triangular field of sides 150 m, 120 m and 180 m. He decided to fence the land 3 times with wire.
aWrite a formula to find the perimeter of a triangle having sides a, b and c. [1 K]
bFind the perimeter of McDonald's field. [1 U]
cFind the total cost of fencing at Rs 10 per metre. [2 A]
dOld McDonald found 2700 m of wire in his warehouse. How many turns in total can the field be fenced? [1 HA]
K: 1U: 1A: 2HA: 1Total: 5 marks
Set 2Pawan has a triangular shaped vegetable garden at the backyard. The sides of the garden are in ratio 2 : 3 : 5. The perimeter of the vegetable garden is 400 m.
aWrite the sides of the triangular garden in terms of x. [1 K]
bFind the value of x. [1 U]
cFind the cost of fencing the garden 5 times at the rate of Rs 5 per metre. [2 A]
dWill Rs 13,000 be enough to fence only 3 times at the rate of Rs 5 per metre? Justify your answer. [1 HA]
K: 1U: 1A: 2HA: 1Total: 5 marks
Set 3Tejus has a triangular field of sides 60 m, 55 m and a third unknown side. The perimeter of the field is 200 m.
aIn the formula T.C = R × L, what does 'L' mean? [1 K]
bFind the measurement of the third side. [1 U]
cFind the total cost of fencing the field 4 times at Rs 20 per metre. [2 A]
dIf cost of wire is reduced by Rs 5 per metre, how much money will be saved? [1 HA]
K: 1U: 1A: 2HA: 1Total: 5 marks
Set 4The ratio of sides of a triangular park is 1 : 3 : 5 and the length of the longest side is 100 m. The park is to be fenced 5 times by a wire.
aIn formula L = n × p, what does 'n' mean? [1 K]
bFind the measurement of the remaining two sides. [1 U]
cHow long the wire must be to fence 5 times? [2 A]
dWill Rs 10,000 be enough to fence the park 5 times at Rs 10 per metre? Justify your answer. [1 HA]
K: 1U: 1A: 2HA: 1Total: 5 marks
Set 5Janaki has two farms as shown in the figures below.
aWrite a formula to calculate the perimeter of an isosceles triangle having equal side 'a' and base 'b'. [1 K]
bFind the perimeter of triangle ABC. [1 U]
cHow long a wire is needed to fence the farm ABC 3 times? Calculate its cost at Rs 5 per metre. [2 A]
dJanaki says, "Remaining side of my farm PQR is equal to the side PR." Explain the relationship between the perimeter of farm ABC and farm PQR. [1 HA]
K: 1U: 1A: 2HA: 1Total: 5 marks
Set 6Popat Lal bought a triangular land from Jethalal. The sides of the land are 60 m, 80 m and 100 m.
aHow can perimeter be defined in one sentence? [1 K]
bFind the perimeter of land bought by Popat Lal. [1 U]
cIt costs Rs 16,000 to fence the land 5 times by a wire. Calculate the rate of wire per metre. [2 A]
dThere was an error while measuring a land. Instead of 70 m it was 60 m. How much more wire will be needed to fence the land? [1 HA]
K: 1U: 1A: 2HA: 1Total: 5 marks
Set 7A triangular garden has sides in ratio 3 : 4 : 5. The shortest side measures 18 m. The garden owner wants to plant a hedge along its boundary twice.
aState the formula to find the perimeter of a scalene triangle with sides p, q and r. [1 K]
bFind all three sides of the triangular garden. [1 U]
cFind the total length of hedge needed and its cost if planting costs Rs 15 per metre. [2 A]
dIf the owner's budget is Rs 3,000, will it be enough to plant the hedge twice? How much extra is needed or how much is saved? [1 HA]
K: 1U: 1A: 2HA: 1Total: 5 marks
Set 8A triangular plot of land has a perimeter of 540 m. Two of its sides measure 190 m and 175 m. The plot is to be fenced with barbed wire that comes in rolls of 50 m each.
aWrite the formula used to find the missing side of a triangle when perimeter and two sides are known. [1 K]
bFind the third side of the triangular plot. [1 U]
cHow many full rolls of wire are needed to fence the plot once? What is the total cost if each roll costs Rs 250? [2 A]
dIf the plot is fenced 4 times, how many rolls are needed and what is the total cost? Will any wire be left over? [1 HA]
K: 1U: 1A: 2HA: 1Total: 5 marks
Set 9An equilateral triangular field has a perimeter of 360 m. The field is to be fenced 6 times with wire costing Rs 8 per metre.
aWhat is special about the sides of an equilateral triangle? Write a formula for its perimeter using side 'a'. [1 K]
bFind the length of each side of the field. [1 U]
cFind the total length of wire required and the total cost of fencing the field 6 times. [2 A]
dIf the cost per metre is increased by Rs 2, how much additional money would be needed to fence the field 6 times? [1 HA]
K: 1U: 1A: 2HA: 1Total: 5 marks
Set 10Ram's farm is triangular in shape with sides 85 m, 110 m and 95 m. His neighbour Shyam's farm is also triangular with sides 105 m, 80 m and 100 m. Both want to fence their farms 3 times.
aDefine perimeter in your own words and write the formula for the perimeter of a triangle. [1 K]
bFind the perimeter of both Ram's and Shyam's farms. [1 U]
cWire costs Rs 12 per metre. Who spends more on fencing their farm 3 times, and by how much? [2 A]
dRam and Shyam decide to pool their money. If they have Rs 25,000 together, can they both fence their farms 3 times? Show your working. [1 HA]