Question

solve the following mentally:
1.) the diagonal of a square is 7√2. find the length of each side.
2.) the altitude of an equilateral triangle measures 6√3. find the length the side.
3.) the perimeter of a square is 32. find the length of its diagonal.
4.) the perimeter of an equilateral triangle is 21. what is the length of its altitude?
5.) the area of a square is 169. what is he length of its diagonal?
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Answer 1

Step-by-step explanation:

A square is a special type of rhombus. And the diagonals of all rhombuses bisect one another at right angles.

So the diagonals divide the rhombus into 4 congruent right angled triangles.

the short sides are each

$7 \times \sqrt{2}$

inches long. And the side of the rhombus is the hypotenuse

${h}^{2} = 7 \sqrt{2} \div 2 \\ \\ {h }^{2} = 2 \\ \\ {h}^{2}$