Question

The resident welfare association of a colony decided to leave a space in the shape of an isosceles triangle of perimeter 36cm and the two equal sides 10cm each for children play activities in the middle of the rectangular park of their neighbourhood. Find the area of the space left for this purpose. What value is indicates from this action?

Answer 1

Please check this answer;

Answer 2

The area of space left for children's play activities is 48cm². This action indicates the value of caring for all age groups in a community.

Given

• Space in the shape of an isosceles triangle
• The perimeter of shape = 36 cm
• 2 equal sides = 10 cm

To Find

Area of the triangle and the value reflected from the problem sum

Solution

Heron's formula for the area of a triangle = $\sqrt{s(s-a)(s-b)(s-c)}$

Where,

• a, b, and c are lengths of three sides of the triangle
• s = semi-perimeter =(a + b + c)/2

According to the problem

Perimeter or, a + b + c = 36 cm

Therefore s = 3/2 cm = 18 cm

We have a = b = 10 cm

Hence, to find c we will use the formula for the perimeter

= a + b + c = 36 cm (Here)

or, 10 + 10 + c = 36

or, 20 + c = 36

or, c = 36 - 20

or, c = 16 cm

Now using all the above results in heron's formula we get

area of park =

$\sqrt{18(18-10)(18-10)(18-16)}$

Solving the brackets we get

$\sqrt{18X8X8X2}$

Now for finding out the square root we first need to prime factorize

$\sqrt{2X3X3X2X2X2X2X2X2X2}$

grouping all the same numbers together we get

$\sqrt{2X2X2X2X2X2X2X2X3X3}$

Now we will further group the numbers into pairs of the same numbers

$\sqrt{(2X2)X(2X2)X(2X2)X(2X2)X(3X3)}$

Taking one number from each pair we get,

2 X 2 X 2 X 2 X 3 cm²

= 48cm²

Hence the area of space left for children's play activities is 48cm². This action indicates the value of caring for all age groups in a community.

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