Question

A kitchen garden is triangular in shape with sides 6m, 8m, 10m. Its owner wants to divide her field into four congruent triangles to grow four different types of flowers on them.
Find the:
i) maximum dimensions of the congruent triangles in which the field can be divided
ii) area of each triangle

Answer 1

Step-by-step explanation:

Given A kitchen garden is triangular in shape with sides 6m, 8m, 10m. Its owner wants to divide her field into four congruent triangles to grow four different types of flowers on them.

Find the:

i) maximum dimensions of the congruent triangles in which the field can be divided

ii) area of each triangle

• Sides of triangle is 6 m,8 m,10 m
• Now area of triangular garden = √s(s – a)(s – b)(s – c)
• Also s = a + b + c / 2 = 6 + 8 + 10 / 2 = 12
• So area = √12(12 – 6)(12 – 8)(12 – 10)
•             = √12 x 6 x 4 x 2
•            = √576
•             = 24 cm^2
• According to question owner wants to divide into 4 congruent triangles.so maximum dimension is possible when triangle is divided into equilateral triangle.
• Therefore area of one equilateral triangle = 24 / 4 = 6 cm^2
• Dimension of equilateral triangle = a
• Area of triangle = √3 / 4 a^2
•        6 = √3 / 4 a^2
•      24 = √3 a^2
• Or a^2 = 24 / √3
• Or a = √13,85 cm
• Or a = 3.721 cm

Reference link will be

https://brainly.in/question/5468510

https://brainly.in/question/11320129