Triangle ABC IS an isosceles triangle AB=BC m
1 answer:
Answer:
<em>The measure of angle A is 73°</em>
Step-by-step explanation:
<u>Isosceles Triangles</u>
An isosceles triangle is a triangle with exactly two congruent sides. The angles the congruent sides form with the third side are also equal.
The triangle ABC is isosceles and AB congruent with BC. The angle at B measures 34°.
The other two angles are congruent, i.e. their measures are the same. Since the internal angles of a triangle sum 180°:
Thus:
The measure of angle A is 73°
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Part 1
<h3>Answer: (x+5)(x+10) - 50 = 126</h3>Other answers are possible.
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Explanation:
The old width was 5, but then it increases to x+5. The old length was 10, but now it's x+10.
The area of any rectangle is length times width.
So the area of the larger rectangle is (x+5)(x+10). Subtract off the old area of 5*10 = 50 and we get (x+5)(x+10) - 50 as the area of the L shape. Set this equal to 126 to finish setting up the equation. This is one possible answer out of many others. This is because we could expand out the (x+5)(x+10) into x^2+10x+5x+50 or simplify that to x^2+15x+50, as two possible options.
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Part 2
<h3>Answer: x = 6</h3>-------------
Explanation:
Solve the equation we set up in the previous part
(x+5)(x+10) - 50 = 126
x^2+10x+5x+50-50 = 126
x^2+15x = 126
x^2+15x-126 = 0
Apply the quadratic formula from here
Another method you could use is factoring, so you could say:
x^2+15x-126 = 0
(x-6)(x+21) = 0
x-6 = 0 or x+21 = 0
x = 6 or x = -21
The issue with this is that it may take a while to do this trial and error approach.
Whichever method you used, you'll end up with two solutions. One of those solutions doesn't make sense though. We can't have a negative length or distance value, so we ignore x = -21.
The only practical solution is x = 6
If x = 6, then the old height goes from 5 to x+5 = 6+5 = 11
If x = 6, then the old length goes from 10 to x+10 = 6+10 = 16
The new larger rectangle is 11*16 = 176 sq ft, in which we subtract off the 50 sq ft to get 176-50 = 126 sq ft, and this matches with the 126 given to us. Therefore, the answer is confirmed.