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Step-5

Title: Triangles

Grade: 8-a Lesson: S2-L5

Explanation: Let us verify the answer here with the steps.

Description:

Explanation	Answer
Problem	Find the area and perimeter of a right angled triangle with sides of lengths 0.9 ft and 1.2 ft.
Formula used	\$"Area" = 1/2 \times ("side")^2\$
Step - 1	Let a, b are the sides and h be the hypotenuse. ⇒ a = 0.9 ft, b = 1.2 ft,
Step - 2	\$"Area" = 1/2 \times ("side")^2\$ ⇒ \$"Area" = 1/\cancel2^1 \times 0.9 \times \cancel(1.2)^0.6\$ ⇒ \$"Area" = 0.54\$
Step - 3	\$"Perimeter" = "side" + "side" + "hypotenuse"\$ ⇒ Perimeter = \$0.9 + 1.2 + \sqrt((0.9)^2 + (1.2)^2)\$ ⇒ Perimeter = \$2.1 + \sqrt(0.81 + 1.44)\$ ⇒ Perimeter = \$2.1 + \sqrt(2.25)\$ ⇒ Perimeter = \$2.1 + 1.5\$ Perimeter = \$3.6\$
Step - 4	Hence, area and perimeter of a right angled triangle are \$0.54\$ and \$3.6\$

Explanation

Answer

Problem

Find the area and perimeter of a right angled triangle with sides of lengths 0.9 ft and 1.2 ft.

Formula used

\$"Area" = 1/2 \times ("side")^2\$

Step - 1

Let a, b are the sides and h be the hypotenuse.

⇒ a = 0.9 ft, b = 1.2 ft,

Step - 2

\$"Area" = 1/2 \times ("side")^2\$

⇒ \$"Area" = 1/\cancel2^1 \times 0.9 \times \cancel(1.2)^0.6\$

⇒ \$"Area" = 0.54\$

Step - 3

\$"Perimeter" = "side" + "side" + "hypotenuse"\$

⇒ Perimeter = \$0.9 + 1.2 + \sqrt((0.9)^2 + (1.2)^2)\$

⇒ Perimeter = \$2.1 + \sqrt(0.81 + 1.44)\$

⇒ Perimeter = \$2.1 + \sqrt(2.25)\$

⇒ Perimeter = \$2.1 + 1.5\$

Perimeter = \$3.6\$

Step - 4

Hence, area and perimeter of a right angled triangle are \$0.54\$ and \$3.6\$