Question

8. A triangle has sides with lengths of 6, 8, and 10 units, and a square has a

perimeter of 28 units. What is the positive difference, in square units,
between the area of the triangle and the area of the square?
a. 1
b. 4
c. 25
d. 100
e. 148

Answer 1

Difference between the area of the triangle and square is 25

Explanation:

• Step 1: Find the area of the triangle given its 3 sides using the Heron's formula.

Area of the triangle =
`√(s (s-a)(s-b)(s-c))` where s =
`(a + b + c)/(2)`

⇒ s = (6 + 8 + 10)/2 = 24/2 = 12

`√(s(s-a)(s-b)(s-c))` =
`√(12(12-6)(12-8)(12-10))`

=
`√(12(6)(4)(2))` =
`√(576)` = 24 sq. units

• Step 2: Find the area of the square with perimeter = 28 units.

Perimeter of the square = 4 × side = 28

⇒ Side of the square = 28/4 = 7 units

⇒ Area of the square = (side)² = 7² = 49 sq. units

• Step 3: Find the difference between the area of the square and triangle.

Difference = 49 - 24 = 25