The side lengths of a square are 7 in. What is the length of the diagonal?

See diagram

look a right triangle

for a right triangle

with legs legnth a and b and hypotonuse c

a²+b²=c²

so

the legs are 7 and the diagonal is c

a=b since all 4 sides of a square are equal legnth

7²+7²=c²

49+49=c²

98=c²

sqrt both sides

√98=c

(√49) (√2) = c

(7) (√2) = c

7√2=c

the legnth of the diagonal is 7√2 inches or aprox 9.899 inches