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Grace [21]
2 years ago
15

PLEASE HEELPPPPPP in circle A, AT = AE =7cm & BR= 48 CM FIND AS​

Mathematics
1 answer:
sineoko [7]2 years ago
5 0

Answer:

Step-by-step explanation:

Comments

AE = AT = 7                                                  Given

AT is a perpendicular bisector of OS        Property of a circle

AE is a perpendicular bisector of BR        Property of a circle

ER = 1/2 BR = 48/2 = 24                              Property of a bisector

TS = ER                                                        Property of a bisector and chord

TS = 24                                                        ER = 24 so TS = 24

AS^2 = TS^2 + TA^2                                   Pythagorean Theorem + rt angle

AS^2 = 24^2 + 7^2                                      Substitute values

AS^2 = 576 + 49                                         Combine

AS^2 = 625                                                 Take sqrt of both sides

√AS^2 = √625                                  

AS = 25

Answer

AS = 25

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In order to begin we must start off with the formula for the area of a triangle, which is a=1/2b(h) where a is area, b is base, and h is height.

In this scenario, we know that the area is 45cm^2 and the base is 2h+12 (since it is twice it’s height plus twelve). We can plug this into the area equation and then proceed to solve out accordingly.
a=1/2b(h)
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Simplify by dividing the two out.

h^2 + 6h - 45 = 0.

Now plug into the quadratic formula (with a=1, b=6, and c=-45) as shown in the image below.

After plugging the equation in and solving, we come to the idea that h is roughly equal to 4.34. We can now plug this back into the triangle area formula to solve out for b.
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In conclusion;
The height is ≈ 4.34
The base is ≈ 8.68

Hope this helps :)
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