If ABCD is a square and AB = 10, what is the measure of CE to the nearest hundredth?
1 answer:
Answer:
Step-by-step explanation:
<em><u>The correct question is </u></em>
If ABCD is a square and AB = 10, what is the measure of AC? (rounded to the nearest hundredth)
see the attached figure to better understand the problem
we know that
All four sides of the square are congruent and all four interior angles are equal to 90°.
so
AB=BC=CD=AD
In the right triangle ACD
Applying the Pythagorean Theorem
we have that
substitute the given value
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Note necessary facts about isosceles triangle ABC:
- The median CD drawn to the base AB is also an altitude to tha base in isosceles triangle (CD⊥AB). This gives you that triangles ACD and BCD are congruent right triangles with hypotenuses AC and BC, respectively.
- The legs AB and BC of isosceles triangle ABC are congruent, AC=BC.
- Angles at the base AB are congruent, m∠A=m∠B=30°.
1. Consider right triangle ACD. The adjacent angle to the leg AD is 30°, so the hypotenuse AC is twice the opposite leg CD to the angle A.
AC=2CD.
2. Consider right triangle BCD. The adjacent angle to the leg BD is 30°, so the hypotenuse BC is twice the opposite leg CD to the angle B.
BC=2CD.
3. Find the perimeters of triangles ACD, BCD and ABC:
4. If sum of the perimeters of △ACD and △BCD is 20 cm more than the perimeter of △ABC, then
5. Since AC=BC=2CD, then the legs AC and BC of isosceles triangles have length 20 cm.
Answer: 20 cm.