Hadi earned $120.00 from his job yesterday. Today he expects to earn 15% less than yesterday and tomorrow he expects to earn 15%
2 answers:
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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.
<h2>Answer:</h2><h2>Step-by-step explanation:</h2>
I've drawn a graph in order to a better understanding of this problem. We know that:
BC is perpendicular to AC
∠DBE = 2x - 1
∠CBE = 5x - 42
Let's call the intersection of line BC and AC the point P, so:
∠P=90°
And points B, P and C form the triangle ΔBPC. On the other hand, ∠CBE and ∠PCB are Alternate Interior Angles, so:
∠PCB = ∠CBE = 5x - 42
Moreover:
∠PBC = 2x - 1 - (5x - 42)
∠PBC = 2x - 1 - 5x + 42
∠PBC = -3x + 41
The internal angles of any triangle add up to 180°. Hence for ΔBPC:
90° + ∠PBC + ∠PCB = 180°
90° - 3x + 41 + 5x - 42 = 180°
2x + 89 = 180
2x = 91
x = 45.5°