Question

An advertising board is in the form of an isosceles triangle with its side 12 m, 10 m and 10 m long. Find the cost of painting it at ₹2 per m².

Answer 1

Answer:

96 rupees

Step-by-step explanation:

Given :

Base of the triangle = 12 metres

Equal sides = 10 metres

To find :

Cost of painting at rs. 2 per m²

Area of a triangle = ½×b×h

Now height can be found with pythogoras theorem

Dividing into half the base of triangle should be 6m

10²=6²+height²

100=36+height²

Height²=100-36

Height²=64

Height = 8

Area of the triangle = ½×12×8

Area of the triangle =6×8

Area of the triangle = 48 m²

Cost per m² = rs. 2

Cost of painting the triangle at rs. 2 per m² = 48×2

Cost of painting the triangle at rs. 2 per m² = 96 rupees

The cost is rupees 96

Answer 2

${ \tt{ \huge{ \underline{ \red{Question:-}}}}}$




▪ An advertising board is in the form of an Isosceles triangle with its side 12 m, 10 m and 10 m long. Find the cost of painting it at Rs. 2 per square metre.



${ \huge{ \tt{ \underline{ \red{Solution:-}}}}}$




${ \dagger{ \purple{ \bold{ \: \: \: GIVEN- }}}}$




${ \underline{ \sf{ \pink{dimension \: of \: advertising \: board}}}} \\ { \red{ \sf{(isosceles \: triangle)}}}$




$\star{ \blue{ \sf{ \: \: base = 12 \: m}}}$




${ \star{ \blue{ \sf{ \: \: 2 \: equal \: sides = 10 \: m}}}}$



${ \dagger{ \purple{ \bold{ \: \: \: TO \: FIND- }}}}$



▪ cost of painting the advertising board at the rate of Rs. 2 per square metre??




${ \rm{ \red{ \underline{ \underline{ area \: of \: triangle}}}}}$




${ \underline{ \boxed{ \sf{ \pink{area = \frac{1}{2} base \times height}}}}}$




▪ using PYTHAGORAS THEOREM for calculating the height of the triangle....



${ \purple{ \tt{ \underline{pythagoras \: theorem}}}} \\ \\ { \red{ \sf{ \rightarrow{ {hypotenuse}^{2} = {base}^{2} + {height}^{2} }}}}$




▪ putting the above given values in the formula...




${ \blue{ \sf{ {10}^{2} = {6}^{2} + {height}^{2}}}}$




${ \implies{ \blue{ \sf{ {height}^{2} = {10}^{2} - {6}^{2} }}}}$




${ \implies{ \blue{ \sf{height = \sqrt{100 - 36}}}}}$




$\implies{ \blue{ \sf{height = \sqrt{64}}}}$



${ \implies{ \red{ \sf{height = 8 \: m}}}}$




▪ now, putting the values of base and height in the formula for area of triangle....




${ \purple{ \sf{ \rightarrow{area = \frac{1}{2} base \times height}}}}$




${ \implies{ \purple{ \sf{area = \frac{1}{2} \times 12 \: m \times 8 \: m}}}}$





${ \implies{ \purple{ \sf{ area = 6 \: m \times 8 \: m = 48 \: {m}^{2}}}}}$




${ \sf{ \pink{rate \: of \: painting = \: Rs. \: 2 \: per \: {m}^{2} }}}$




${ \red{ \sf{ cost \: of \: painting = Rs . \: \frac{2}{ {m}^{2} } \times area}}}$





${ \implies{ \red{ \sf{cost \: of \: painting = Rs. \: \frac{2}{ {m}^{2} } \times 48 \: {m}^{2} }}}}$




therefore,



${ \boxed{ \boxed{ \blue{ \sf{cost \: of \: painting = \: Rs . \: 96}}}}}$