Question

Find the diagonal of a square whose area is 64 m².
the length​

Answer 1

Answer:

side of square =8m

length of diagonal=√2 a

√2*8

11.3 is the length of diagonal

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Answer 2

The diagonal of a square who has area of 64 m² will be 11.31 m.

Step-by-step explanation:

${\underline{\underline{\bf{Given:}}}}$

• The area of a square is 64 m²

${\underline{\underline{\bf{To\:find:}}}}$

• The length of the diagonal of the square.

${\underline{\underline{\bf{Formula\:to\:be\: used:}}}}$

$\underline{\boxed{\sf{{Area}_{[Square]}=a^2\:sq.units}}}$

$\underline{\boxed{\sf{{Diagonal}_{[Square]}=\sqrt{2}a\:units}}}$

$\:\:\:\:\:\:\:\:\:\mapsto{\sf{a=side}}$

${\underline{\underline{\bf{Solution:}}}}$

‎ ‎ ‎ ‎ ‎ ‎ ‎We can find the length of the diagonal of the square by inserting the measure of its side in the formula $\bf{[\sqrt{2}a\:units]}$

But, we are only given with the measure of area of the square. So, first let us find the measure of its side by inserting the measure of area in the formula:

$\leadsto{\bf{\purple{Area=a^2\:sq.units}}}$

$\:$

$\:\:\:\:\:\:\::\implies{\sf{64=a^2}}$

$\:\:\:\:\:\:\::\implies{\sf{\sqrt{64}=a}}$

$\:\:\:\:\:\:\::\implies\underline{\bf{8\:m=a}}$

$\:$

$\:\:\:\:\:\:\:\:\:\small{\boxed{\sf{Side\:of\: the \:square\:is\:8\:m}}}$

Now, by inserting the measure of side in the formula:

$\leadsto{\bf{\purple{\sqrt{2}a\:units}}}$

$\:$

$\:\:\:\:\:\:\:\:\::\implies{\sf{\sqrt{2}\times 8}}$

$\:\:\:\:\:\:\:\:\::\implies{\boxed{\frak{\red{11.31\:m}}}}$

Alternate method:

If we look at the diagram (attachment)! We can see that the side $\sf{\overline{CD}}$ forms as the base of a right-angled triangle whereas, the side $\sf{\overline{BD}}$ forms as the perpendicular of the triangle. Also, the the diagonal $\sf{\overline{BC}}$ forms as the hypotenuse of the triangle.

We need the measure of length of the diagonal. So, we can find it using Pythagorean Theorem. The length of base and perpendicular equals the length of side of the square.

$\leadsto{\boxed{\bf{\purple{a^2+b^2=c^2}}}}$

$\:\:\:\:\:\:\:\:\:\mapsto{\sf{a=Base}}$

$\:\:\:\:\:\:\:\:\:\mapsto{\sf{b=Perpendicular}}$

$\:\:\:\:\:\:\:\:\:\mapsto{\sf{c=Hypotenuse}}$

$\:$

$\:\:\:\:\:\:\:\:\::\implies{\sf{8^2+8^2=c^2}}$

$\:\:\:\:\:\:\:\:\::\implies{\sf{64+64=c^2}}$

$\:\:\:\:\:\:\:\:\::\implies{\sf{128=c^2}}$

$\:\:\:\:\:\:\:\:\::\implies{\sf{\sqrt{128}=c}}$

$\:\:\:\:\:\:\:\:\::\implies{\boxed{\frak{\red{11.31\:m=c}}}}$

$\:\:\:\:\:\:\:\:\::\implies{\bf{c=Diagonal}}$

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