Question

There is a slide in a Park which is to be painted by 10 students with white colour written as "KEEP 6 FEET DISTANCE" If the sides of triangular park is 15 cms, 11 cms and 6 cms respectively. Calculate the are of park. If the cost of painting is Rs. 10/-. How much amount will each student have to bear.​

Answer 1

Answer:

Area of triangle =

$20 \sqrt{2} \: cm {}^{2}$

Cost of painting per student = 89.44 Rs per student

Step By Step Explanation:

we have given that

A = 15 cm B = 11 cm C = 6 cm and

cost of painting per cm^2 = 10 RS

To find the cost per student will be paying we first need to find the area of the park so,

Area of a Triangle =

$\sqrt{s(s - a)(s - b)(s - c)}$

here s is semi perimeter (half of perimeter)

semi perimeter =

$(a + b + c) \: \div \: 2$

so to find the area we first have to find the semi perimeter

semi perimeter = (15 + 11 + 6) ÷ 2

= 32 ÷ 2

s = 16 cm

so now we can find the area of triangle

area of triangle =

$\sqrt{s(s - a)(s - b)(s - c)}$

$\sqrt{16(16 - 15)(16 - 11)(16 - 6)}$

$\sqrt{16 \times 1 \times 5 \times 10}$

now we will be taking out the factors of each and make a pair of same number so that the paired number can be taken out from under root

$\sqrt{4 \times 4 \times 1 \times 5 \times 5 \times 2}$

so here there are two pair one pair of 4 and one pair of 5 so we will take out those two number from under root and writ it once

$4 \times 5 \times \sqrt{2 \times 1}$

$20 \sqrt{2} \: cm {}^{2}$

now to find the cost of painting which is. 10rs per cm^2 we will multiply the area with the cost which is 10 to find the cost of painting for 20root 2 cm^2

$10 \times (20 \sqrt{2} )$

$20 \times 10 \: \sqrt{2 \times 10}$

$200 \sqrt{20}$

now again we will remove the pair from under root of 20

$200 \times \sqrt{2 \times 2 \times 5}$

$200 \: \times 2 \sqrt{5}$

$40 \sqrt{5}$

so to find Rs we need to find the value of root 5 and multiply by 400. value of root 5 = 2.2360

= 400 × 2.2360

= 894.4 Rs

now we have to divide it between 10 student as asked in the question so ,

= 894.4 ÷ 10

= 89.44 Rs per student

Answer 2

Answer:

the answer will be 20root 2 and rs is 89.44