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Step-4

Title: Squares

Grade: 8-a Lesson: S2-L7

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

Description:

Explanation	Answer
Problem	A field has an area of 121 square feet. Find the distance between opposite corners.
Formula used	\$"Diagonal of Square" = a \times \sqrt2\$
Step - 1	Given that, Area of square = 121 square feet
Step - 2	Area = \$a^2\$ ⇒ 121 = \$a^2\$ ⇒ \$\sqrt(121) = a\$ ⇒ a = 11
Step - 3	We know that, \$"Diagonal of Square" = a \times \sqrt2\$ \$"Diagonal of Square" = 11 \times \sqrt2\$ \$"Diagonal of Square" = 11 \sqrt2\$
Step - 4	Hence, the distance between opposite corners is \$11 \sqrt2\$

Explanation

Answer

Problem

A field has an area of 121 square feet. Find the distance between opposite corners.

Formula used

\$"Diagonal of Square" = a \times \sqrt2\$

Step - 1

Given that,

Area of square = 121 square feet

Step - 2

Area = \$a^2\$

⇒ 121 = \$a^2\$

⇒ \$\sqrt(121) = a\$

⇒ a = 11

Step - 3

We know that,

\$"Diagonal of Square" = a \times \sqrt2\$

\$"Diagonal of Square" = 11 \times \sqrt2\$

\$"Diagonal of Square" = 11 \sqrt2\$

Step - 4

Hence, the distance between opposite corners is \$11 \sqrt2\$